YES 46.396 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
  ((intersectFM_C :: (Ord b, Ord a) => (e  ->  c  ->  d)  ->  FiniteMap (Either b a) e  ->  FiniteMap (Either b a) c  ->  FiniteMap (Either b a) d) :: (Ord b, Ord a) => (e  ->  c  ->  d)  ->  FiniteMap (Either b a) e  ->  FiniteMap (Either b a) c  ->  FiniteMap (Either b a) d)

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 a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM fm key elt = addToFM_C (\old new ->new) fm key elt

  addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt = unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_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

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l
deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r
deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin 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 a b  ->  [(a,b)]
fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm

  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

  glueBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueBal EmptyFM fm2 = fm2
glueBal fm1 EmptyFM = fm1
glueBal fm1 fm2 
 | sizeFM fm2 > sizeFM fm1 = 
mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
 | otherwise = 
mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where 
mid_elt1 = (\(_,mid_elt1) ->mid_elt1) vv2
mid_elt2 = (\(_,mid_elt2) ->mid_elt2) vv3
mid_key1 = (\(mid_key1,_) ->mid_key1) vv2
mid_key2 = (\(mid_key2,_) ->mid_key2) vv3
vv2 = findMax fm1
vv3 = findMin fm2

  glueVBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal 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 (glueVBal fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r)
 | otherwise = 
glueBal fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  intersectFM_C :: Ord c => (d  ->  a  ->  b)  ->  FiniteMap c d  ->  FiniteMap c a  ->  FiniteMap c b
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = (\(Just elt1) ->elt1) vv1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

  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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



Lambda Reductions:
The following Lambda expression
\(mid_key1,_)→mid_key1

is transformed to
mid_key10 (mid_key1,_) = mid_key1

The following Lambda expression
\(_,mid_elt1)→mid_elt1

is transformed to
mid_elt10 (_,mid_elt1) = mid_elt1

The following Lambda expression
\(mid_key2,_)→mid_key2

is transformed to
mid_key20 (mid_key2,_) = mid_key2

The following Lambda expression
\(_,mid_elt2)→mid_elt2

is transformed to
mid_elt20 (_,mid_elt2) = mid_elt2

The following Lambda expression
\(Just elt1)→elt1

is transformed to
elt10 (Just elt1) = elt1

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
  ((intersectFM_C :: (Ord c, Ord d) => (b  ->  e  ->  a)  ->  FiniteMap (Either c d) b  ->  FiniteMap (Either c d) e  ->  FiniteMap (Either c d) a) :: (Ord c, Ord d) => (b  ->  e  ->  a)  ->  FiniteMap (Either c d) b  ->  FiniteMap (Either c d) e  ->  FiniteMap (Either c d) a)

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

  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 = 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

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l
deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r
deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin 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 :: (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

  glueBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueBal EmptyFM fm2 = fm2
glueBal fm1 EmptyFM = fm1
glueBal fm1 fm2 
 | sizeFM fm2 > sizeFM fm1 = 
mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
 | otherwise = 
mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where 
mid_elt1 = mid_elt10 vv2
mid_elt10 (_,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (_,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,_) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,_) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  glueVBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal 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 (glueVBal fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r)
 | otherwise = 
glueBal fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  intersectFM_C :: Ord b => (c  ->  a  ->  d)  ->  FiniteMap b c  ->  FiniteMap b a  ->  FiniteMap b d
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

  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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



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
  ((intersectFM_C :: (Ord a, Ord e) => (b  ->  c  ->  d)  ->  FiniteMap (Either e a) b  ->  FiniteMap (Either e a) c  ->  FiniteMap (Either e a) d) :: (Ord a, Ord e) => (b  ->  c  ->  d)  ->  FiniteMap (Either e a) b  ->  FiniteMap (Either e a) c  ->  FiniteMap (Either e a) d)

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 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

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l
deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r
deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

  glueBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueBal EmptyFM fm2 = fm2
glueBal fm1 EmptyFM = fm1
glueBal fm1 fm2 
 | sizeFM fm2 > sizeFM fm1 = 
mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
 | otherwise = 
mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where 
mid_elt1 = mid_elt10 vv2
mid_elt10 (_,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (_,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,_) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,_) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  glueVBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal 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 (glueVBal fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r)
 | otherwise = 
glueBal fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  intersectFM_C :: Ord d => (c  ->  b  ->  a)  ->  FiniteMap d c  ->  FiniteMap d b  ->  FiniteMap d a
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

  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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



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
  ((intersectFM_C :: (Ord a, Ord e) => (d  ->  b  ->  c)  ->  FiniteMap (Either e a) d  ->  FiniteMap (Either e a) b  ->  FiniteMap (Either e a) c) :: (Ord a, Ord e) => (d  ->  b  ->  c)  ->  FiniteMap (Either e a) d  ->  FiniteMap (Either e a) b  ->  FiniteMap (Either e a) c)

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

  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

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l
deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r
deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

  glueBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueBal EmptyFM fm2 = fm2
glueBal fm1 EmptyFM = fm1
glueBal fm1 fm2 
 | sizeFM fm2 > sizeFM fm1 = 
mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
 | otherwise = 
mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where 
mid_elt1 = mid_elt10 vv2
mid_elt10 (_,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (_,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,_) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,_) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  glueVBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal 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 (glueVBal fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r)
 | otherwise = 
glueBal fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  intersectFM_C :: Ord b => (a  ->  d  ->  c)  ->  FiniteMap b a  ->  FiniteMap b d  ->  FiniteMap b c
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

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

  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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



Replaced joker patterns by fresh variables and removed binding patterns.
Binding Reductions:
The bind variable of the following binding Pattern
fm_l@(Branch yy yz zu zv zw)

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

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

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

The bind variable of the following binding Pattern
fm_l@(Branch vuy vuz vvu vvv vvw)

is replaced by the following term
Branch vuy vuz vvu vvv vvw

The bind variable of the following binding Pattern
fm_r@(Branch vvy vvz vwu vwv vww)

is replaced by the following term
Branch vvy vvz vwu vwv vww



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

mainModule FiniteMap
  ((intersectFM_C :: (Ord a, Ord d) => (b  ->  e  ->  c)  ->  FiniteMap (Either d a) b  ->  FiniteMap (Either d a) e  ->  FiniteMap (Either d a) c) :: (Ord a, Ord d) => (b  ->  e  ->  c)  ->  FiniteMap (Either d a) b  ->  FiniteMap (Either d a) e  ->  FiniteMap (Either d a) c)

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

  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

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt vwx fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwy fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMin (Branch key elt wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vyz vzu EmptyFM) = (key,elt)
findMax (Branch key elt vzv vzw 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 :: (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

  glueBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueBal EmptyFM fm2 = fm2
glueBal fm1 EmptyFM = fm1
glueBal fm1 fm2 
 | sizeFM fm2 > sizeFM fm1 = 
mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
 | otherwise = 
mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where 
mid_elt1 = mid_elt10 vv2
mid_elt10 (vzx,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (vzy,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,vzz) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,wuu) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  glueVBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
 | otherwise = 
glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) where 
size_l = sizeFM (Branch yy yz zu zv zw)
size_r = sizeFM (Branch zy zz vuu vuv vuw)

  intersectFM_C :: Ord a => (d  ->  b  ->  c)  ->  FiniteMap a d  ->  FiniteMap a b  ->  FiniteMap a c
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

  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 vxz (Branch key_rl elt_rl vyu 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 vxu fm_ll (Branch key_lr elt_lr vxv 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 vyv vyw vyx 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 vxw vxx vxy 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 vyy 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 vwz 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 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 = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
 | otherwise = 
mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) where 
size_l = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r = sizeFM (Branch vvy vvz vwu vwv vww)

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



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)

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

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 wzz xuu = splitLT3 wzz xuu

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 xux xuy = splitGT3 xux xuy

The following Function with conditions
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
 | otherwise
 = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)
where 
size_l  = sizeFM (Branch yy yz zu zv zw)
size_r  = sizeFM (Branch zy zz vuu vuv vuw)

is transformed to
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = 
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * size_l < size_r)
where 
glueVBal0 yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)
glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal0 yy yz zu zv zw zy zz vuu vuv vuw otherwise
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch yy yz zu zv zw)
size_r  = sizeFM (Branch zy zz vuu vuv vuw)

glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvw xvx = glueVBal3 xvw xvx

glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

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 vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
 | otherwise
 = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
where 
size_l  = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r  = sizeFM (Branch vvy vvz vwu vwv vww)

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 vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = 
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch0 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r  = sizeFM (Branch vvy vvz vwu vwv vww)

mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy 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 vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx 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 vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx 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 vxz (Branch key_rl elt_rl vyu 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 vxu fm_ll (Branch key_lr elt_lr vxv 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 vyv vyw vyx 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 vxw vxx vxy 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 vyy 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 vwz 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 vxz (Branch key_rl elt_rl vyu 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 vxu fm_ll (Branch key_lr elt_lr vxv 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 vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy 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 vyy 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 vwz 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_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_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise

addToFM_C3 combiner (Branch key elt size fm_l fm_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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

The following Function with conditions
glueBal EmptyFM fm2 = fm2
glueBal fm1 EmptyFM = fm1
glueBal fm1 fm2
 | sizeFM fm2 > sizeFM fm1
 = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
 | otherwise
 = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2
where 
mid_elt1  = mid_elt10 vv2
mid_elt10 (vzx,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (vzy,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,vzz) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,wuu) = mid_key2
vv2  = findMax fm1
vv3  = findMin fm2

is transformed to
glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2
glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM
glueBal fm1 fm2 = glueBal2 fm1 fm2

glueBal2 fm1 fm2 = 
glueBal1 fm1 fm2 (sizeFM fm2 > sizeFM fm1)
where 
glueBal0 fm1 fm2 True = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2
glueBal1 fm1 fm2 True = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
glueBal1 fm1 fm2 False = glueBal0 fm1 fm2 otherwise
mid_elt1  = mid_elt10 vv2
mid_elt10 (vzx,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (vzy,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,vzz) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,wuu) = mid_key2
vv2  = findMax fm1
vv3  = findMin fm2

glueBal3 fm1 EmptyFM = fm1
glueBal3 xzy xzz = glueBal2 xzy xzz

glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

The following Function with conditions
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find
 | key_to_find < key
 = lookupFM fm_l key_to_find
 | key_to_find > key
 = lookupFM fm_r key_to_find
 | otherwise
 = Just elt

is transformed to
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

The following Function with conditions
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right)
 | Maybe.isJust maybe_elt1
 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise
 = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
where 
elt1  = elt10 vv1
elt10 (Just elt1) = elt1
gts  = splitGT fm1 split_key
lts  = splitLT fm1 split_key
maybe_elt1  = lookupFM fm1 split_key
vv1  = maybe_elt1

is transformed to
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = 
intersectFM_C1 combiner fm1 split_key elt2 wuy left right (Maybe.isJust maybe_elt1)
where 
elt1  = elt10 vv1
elt10 (Just elt1) = elt1
gts  = splitGT fm1 split_key
intersectFM_C0 combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right False = intersectFM_C0 combiner fm1 split_key elt2 wuy left right otherwise
lts  = splitLT fm1 split_key
maybe_elt1  = lookupFM fm1 split_key
vv1  = maybe_elt1

intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

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

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

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 ywy = gcd'2 x ywy
gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x ywy = x
gcd'1 ywz yxu yxv = gcd'0 yxu yxv

gcd'2 x ywy = gcd'1 (ywy == 0) x ywy
gcd'2 yxw yxx = gcd'0 yxw yxx

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 yxy yxz = gcd3 yxy yxz
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x ywy = gcd'2 x ywy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x ywy = x
gcd'1 ywz yxu yxv = gcd'0 yxu yxv
gcd'2 x ywy = gcd'1 (ywy == 0) x ywy
gcd'2 yxw yxx = gcd'0 yxw yxx

gcd1 True yxy yxz = error []
gcd1 yyu yyv yyw = gcd0 yyv yyw

gcd2 True yxy yxz = gcd1 (yxz == 0) yxy yxz
gcd2 yyx yyy yyz = gcd0 yyy yyz

gcd3 yxy yxz = gcd2 (yxy == 0) yxy yxz
gcd3 yzu yzv = gcd0 yzu yzv

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
  ((intersectFM_C :: (Ord c, Ord b) => (d  ->  a  ->  e)  ->  FiniteMap (Either b c) d  ->  FiniteMap (Either b c) a  ->  FiniteMap (Either b c) e) :: (Ord c, Ord b) => (d  ->  a  ->  e)  ->  FiniteMap (Either b c) d  ->  FiniteMap (Either b c) a  ->  FiniteMap (Either b c) e)

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 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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt vwx fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwy fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMin (Branch key elt wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vyz vzu EmptyFM) = (key,elt)
findMax (Branch key elt vzv vzw 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 :: (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

  glueBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2
glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM
glueBal fm1 fm2 = glueBal2 fm1 fm2

  
glueBal2 fm1 fm2 = 
glueBal1 fm1 fm2 (sizeFM fm2 > sizeFM fm1) where 
glueBal0 fm1 fm2 True = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2
glueBal1 fm1 fm2 True = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
glueBal1 fm1 fm2 False = glueBal0 fm1 fm2 otherwise
mid_elt1 = mid_elt10 vv2
mid_elt10 (vzx,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (vzy,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,vzz) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,wuu) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzy xzz = glueBal2 xzy xzz

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

  glueVBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = 
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * size_l < size_r) where 
glueVBal0 yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)
glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal0 yy yz zu zv zw zy zz vuu vuv vuw otherwise
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * size_r < size_l)
size_l = sizeFM (Branch yy yz zu zv zw)
size_r = sizeFM (Branch zy zz vuu vuv vuw)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvw xvx = glueVBal3 xvw xvx

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

  intersectFM_C :: Ord c => (b  ->  a  ->  d)  ->  FiniteMap c b  ->  FiniteMap c a  ->  FiniteMap c d
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = 
intersectFM_C1 combiner fm1 split_key elt2 wuy left right (Maybe.isJust maybe_elt1) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
intersectFM_C0 combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right False = intersectFM_C0 combiner fm1 split_key elt2 wuy left right otherwise
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  
intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

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

  
mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu 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 vxu fm_ll (Branch key_lr elt_lr vxv 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 vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy 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 vyy 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 vwz 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 vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = 
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * size_l < size_r) where 
mkVBalBranch0 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch0 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * size_r < size_l)
size_l = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r = sizeFM (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

  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 xux xuy = splitGT3 xux xuy

  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 wzz xuu = splitLT3 wzz xuu

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



Let/Where Reductions:
The bindings of the following Let/Where expression
intersectFM_C1 combiner fm1 split_key elt2 wuy left right (Maybe.isJust maybe_elt1)
where 
elt1  = elt10 vv1
elt10 (Just elt1) = elt1
gts  = splitGT fm1 split_key
intersectFM_C0 combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right False = intersectFM_C0 combiner fm1 split_key elt2 wuy left right otherwise
lts  = splitLT fm1 split_key
maybe_elt1  = lookupFM fm1 split_key
vv1  = maybe_elt1

are unpacked to the following functions on top level
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 yzw yzx) elt2) (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right otherwise

intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)

intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

intersectFM_C2Gts yzw yzx = splitGT yzw yzx

intersectFM_C2Elt1 yzw yzx = intersectFM_C2Elt10 yzw yzx (intersectFM_C2Vv1 yzw yzx)

intersectFM_C2Lts yzw yzx = splitLT yzw yzx

The bindings of the following Let/Where expression
glueBal1 fm1 fm2 (sizeFM fm2 > sizeFM fm1)
where 
glueBal0 fm1 fm2 True = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2
glueBal1 fm1 fm2 True = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
glueBal1 fm1 fm2 False = glueBal0 fm1 fm2 otherwise
mid_elt1  = mid_elt10 vv2
mid_elt10 (vzx,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (vzy,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,vzz) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,wuu) = mid_key2
vv2  = findMax fm1
vv3  = findMin fm2

are unpacked to the following functions on top level
glueBal2Vv2 yzy yzz = findMax yzy

glueBal2Vv3 yzy yzz = findMin yzz

glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz)

glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2)
glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise

glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz)

glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz)

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 vxz (Branch key_rl elt_rl vyu 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 vxu fm_ll (Branch key_lr elt_lr vxv 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 vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy 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 vyy 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 vwz 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
mkBalBranch6Double_L zuu zuv zuw zux fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 zuu zuv fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_r zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_l zuu zuv zuw zux)

mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R otherwise

mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_l zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_r zuu zuv zuw zux)

mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6Double_R zuu zuv zuw zux (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 zuu zuv fm_lrr fm_r)

mkBalBranch6Single_L zuu zuv zuw zux fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zuu zuv fm_l fm_rl) fm_rr

mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

mkBalBranch6Single_R zuu zuv zuw zux (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 zuu zuv fm_lr fm_r)

mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

The bindings of the following Let/Where expression
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * size_l < size_r)
where 
glueVBal0 yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)
glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal0 yy yz zu zv zw zy zz vuu vuv vuw otherwise
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal2 yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal1 yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch yy yz zu zv zw)
size_r  = sizeFM (Branch zy zz vuu vuv vuw)

are unpacked to the following functions on top level
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv < glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv)

glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zuy zuz zvu zvv zvw)

glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zvx zvy zvz zwu zwv)

glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw otherwise

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_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchBalance_ok zww zwx zwy = True

mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchLeft_size zww zwx zwy = sizeFM zww

mkBranchUnbox zww zwx zwy x = x

mkBranchRight_ok zww zwx zwy = mkBranchRight_ok0 zww zwx zwy zwx zwy zwx

mkBranchLeft_ok zww zwx zwy = mkBranchLeft_ok0 zww zwx zwy zww zwy zww

mkBranchRight_size zww zwx zwy = sizeFM zwx

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 zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zxw zwz (1 + mkBranchLeft_size zxv zxw zwz + mkBranchRight_size zxv zxw zwz)) zxv zxw

The bindings of the following Let/Where expression
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch0 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch2 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch1 key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r  = sizeFM (Branch vvy vvz vwu vwv vww)

are unpacked to the following functions on top level
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu < mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu)

mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zyw zyx zyy zyz zzu)

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 zzv = fst (findMax zzv)

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 zzw = fst (findMin zzw)

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

are unpacked to the following functions on top level
reduce2D zzx zzy = gcd zzx zzy

reduce2Reduce1 zzx zzy x y True = error []
reduce2Reduce1 zzx zzy x y False = reduce2Reduce0 zzx zzy x y otherwise

reduce2Reduce0 zzx zzy x y True = x `quot` reduce2D zzx zzy :% (y `quot` reduce2D zzx zzy)

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x ywy = gcd'2 x ywy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x ywy = x
gcd'1 ywz yxu yxv = gcd'0 yxu yxv
gcd'2 x ywy = gcd'1 (ywy == 0) x ywy
gcd'2 yxw yxx = gcd'0 yxw yxx

are unpacked to the following functions on top level
gcd0Gcd'1 True x ywy = x
gcd0Gcd'1 ywz yxu yxv = gcd0Gcd'0 yxu yxv

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

gcd0Gcd' x ywy = gcd0Gcd'2 x ywy
gcd0Gcd' x y = gcd0Gcd'0 x y

gcd0Gcd'2 x ywy = gcd0Gcd'1 (ywy == 0) x ywy
gcd0Gcd'2 yxw yxx = gcd0Gcd'0 yxw yxx



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

mainModule FiniteMap
  ((intersectFM_C :: (Ord e, Ord c) => (b  ->  a  ->  d)  ->  FiniteMap (Either e c) b  ->  FiniteMap (Either e c) a  ->  FiniteMap (Either e c) d) :: (Ord c, Ord e) => (b  ->  a  ->  d)  ->  FiniteMap (Either e c) b  ->  FiniteMap (Either e c) a  ->  FiniteMap (Either e c) d)

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 = 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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt vwx fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwy fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMin (Branch key elt wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vyz vzu EmptyFM) = (key,elt)
findMax (Branch key elt vzv vzw 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 :: (b  ->  c  ->  a  ->  a)  ->  a  ->  FiniteMap b c  ->  a
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

  glueBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2
glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM
glueBal fm1 fm2 = glueBal2 fm1 fm2

  
glueBal2 fm1 fm2 = glueBal2GlueBal1 fm1 fm2 fm1 fm2 (sizeFM fm2 > sizeFM fm1)

  
glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

  
glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2)
glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise

  
glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

  
glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzy

  
glueBal2Vv3 yzy yzz = findMin yzz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzy xzz = glueBal2 xzy xzz

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

  glueVBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = glueVBal3GlueVBal2 yy yz zu zv zw zy zz vuu vuv vuw yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_l yy yz zu zv zw zy zz vuu vuv vuw < glueVBal3Size_r yy yz zu zv zw zy zz vuu vuv vuw)

  
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw otherwise

  
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv < glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv)

  
glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zuy zuz zvu zvv zvw)

  
glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zvx zvy zvz zwu zwv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvw xvx = glueVBal3 xvw xvx

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

  intersectFM_C :: Ord d => (a  ->  b  ->  c)  ->  FiniteMap d a  ->  FiniteMap d b  ->  FiniteMap d c
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 wuy left right (Maybe.isJust (intersectFM_C2Maybe_elt1 fm1 split_key))

  
intersectFM_C2Elt1 yzw yzx = intersectFM_C2Elt10 yzw yzx (intersectFM_C2Vv1 yzw yzx)

  
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

  
intersectFM_C2Gts yzw yzx = splitGT yzw yzx

  
intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)

  
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 yzw yzx) elt2) (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right otherwise

  
intersectFM_C2Lts yzw yzx = splitLT yzw yzx

  
intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

  
intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

  
intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

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

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

  
mkBalBranch6Double_L zuu zuv zuw zux fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 zuu zuv fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R zuu zuv zuw zux (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 zuu zuv fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_l zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_r zuu zuv zuw zux)

  
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_r zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_l zuu zuv zuw zux)

  
mkBalBranch6Single_L zuu zuv zuw zux fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zuu zuv fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R zuu zuv zuw zux (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 zuu zuv fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

  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 zww zwx zwy = True

  
mkBranchLeft_ok zww zwx zwy = mkBranchLeft_ok0 zww zwx zwy zww zwy zww

  
mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zww

  
mkBranchResult zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zxw zwz (1 + mkBranchLeft_size zxv zxw zwz + mkBranchRight_size zxv zxw zwz)) zxv zxw

  
mkBranchRight_ok zww zwx zwy = mkBranchRight_ok0 zww zwx zwy zwx zwy zwx

  
mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zwx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox zww zwx zwy 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 vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3MkVBalBranch2 vvy vvz vwu vwv vww vuy vuz vvu vvv vvw key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_l vvy vvz vwu vwv vww vuy vuz vvu vvv vvw < mkVBalBranch3Size_r vvy vvz vwu vwv vww vuy vuz vvu vvv vvw)

  
mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

  
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu < mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

  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 = 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 xux xuy = splitGT3 xux xuy

  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 wzz xuu = splitLT3 wzz xuu

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



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
  (intersectFM_C :: (Ord a, Ord b) => (d  ->  e  ->  c)  ->  FiniteMap (Either b a) d  ->  FiniteMap (Either b a) e  ->  FiniteMap (Either b a) c)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap 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 = 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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt vwx fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwy fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

  deleteMin :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMin (Branch key elt wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vyz vzu EmptyFM) = (key,elt)
findMax (Branch key elt vzv vzw 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 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

  glueBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2
glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM
glueBal fm1 fm2 = glueBal2 fm1 fm2

  
glueBal2 fm1 fm2 = glueBal2GlueBal1 fm1 fm2 fm1 fm2 (sizeFM fm2 > sizeFM fm1)

  
glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

  
glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2)
glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise

  
glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

  
glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzy

  
glueBal2Vv3 yzy yzz = findMin yzz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzy xzz = glueBal2 xzy xzz

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

  glueVBal :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3 (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw) = glueVBal3GlueVBal2 yy yz zu zv zw zy zz vuu vuv vuw yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_l yy yz zu zv zw zy zz vuu vuv vuw < glueVBal3Size_r yy yz zu zv zw zy zz vuu vuv vuw)

  
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw otherwise

  
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv < glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv)

  
glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zuy zuz zvu zvv zvw)

  
glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zvx zvy zvz zwu zwv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvw xvx = glueVBal3 xvw xvx

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

  intersectFM_C :: Ord c => (b  ->  a  ->  d)  ->  FiniteMap c b  ->  FiniteMap c a  ->  FiniteMap c d
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 wuy left right (Maybe.isJust (intersectFM_C2Maybe_elt1 fm1 split_key))

  
intersectFM_C2Elt1 yzw yzx = intersectFM_C2Elt10 yzw yzx (intersectFM_C2Vv1 yzw yzx)

  
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

  
intersectFM_C2Gts yzw yzx = splitGT yzw yzx

  
intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)

  
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 yzw yzx) elt2) (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right otherwise

  
intersectFM_C2Lts yzw yzx = splitLT yzw yzx

  
intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

  
intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

  
intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

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

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

  
mkBalBranch6Double_L zuu zuv zuw zux fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu 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))))))) zuu zuv fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R zuu zuv zuw zux (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv 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))))))))))))) zuu zuv fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_l zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_r zuu zuv zuw zux)

  
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_r zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_l zuu zuv zuw zux)

  
mkBalBranch6Single_L zuu zuv zuw zux fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) zuu zuv fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R zuu zuv zuw zux (Branch key_l elt_l vwz 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)))))))))) zuu zuv fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

  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 zww zwx zwy = True

  
mkBranchLeft_ok zww zwx zwy = mkBranchLeft_ok0 zww zwx zwy zww zwy zww

  
mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zww

  
mkBranchResult zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zxw zwz (Pos (Succ Zero) + mkBranchLeft_size zxv zxw zwz + mkBranchRight_size zxv zxw zwz)) zxv zxw

  
mkBranchRight_ok zww zwx zwy = mkBranchRight_ok0 zww zwx zwy zwx zwy zwx

  
mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zwx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox zww zwx zwy 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 vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3MkVBalBranch2 vvy vvz vwu vwv vww vuy vuz vvu vvv vvw key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_l vvy vvz vwu vwv vww vuy vuz vvu vvv vvw < mkVBalBranch3Size_r vvy vvz vwu vwv vww vuy vuz vvu vvv vvw)

  
mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

  
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu < mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

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

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = Pos Zero
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 xux xuy = splitGT3 xux xuy

  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 wzz xuu = splitLT3 wzz xuu

  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
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueBal2Mid_elt20(zzz689, zzz690, zzz691, zzz692, zzz693, zzz694, zzz695, zzz696, zzz697, zzz698, zzz699, zzz700, zzz701, Branch(zzz7020, zzz7021, zzz7022, zzz7023, zzz7024), zzz703, h, ba) → new_glueBal2Mid_elt20(zzz689, zzz690, zzz691, zzz692, zzz693, zzz694, zzz695, zzz696, zzz697, zzz698, zzz7020, zzz7021, zzz7022, zzz7023, zzz7024, h, ba)

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

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



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueBal2Mid_key20(zzz673, zzz674, zzz675, zzz676, zzz677, zzz678, zzz679, zzz680, zzz681, zzz682, zzz683, zzz684, zzz685, Branch(zzz6860, zzz6861, zzz6862, zzz6863, zzz6864), zzz687, h, ba) → new_glueBal2Mid_key20(zzz673, zzz674, zzz675, zzz676, zzz677, zzz678, zzz679, zzz680, zzz681, zzz682, zzz6860, zzz6861, zzz6862, zzz6863, zzz6864, h, ba)

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

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



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueBal2Mid_elt10(zzz722, zzz723, zzz724, zzz725, zzz726, zzz727, zzz728, zzz729, zzz730, zzz731, zzz732, zzz733, zzz734, zzz735, Branch(zzz7360, zzz7361, zzz7362, zzz7363, zzz7364), h, ba) → new_glueBal2Mid_elt10(zzz722, zzz723, zzz724, zzz725, zzz726, zzz727, zzz728, zzz729, zzz730, zzz731, zzz7360, zzz7361, zzz7362, zzz7363, zzz7364, h, ba)

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

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



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueBal2Mid_key10(zzz705, zzz706, zzz707, zzz708, zzz709, zzz710, zzz711, zzz712, zzz713, zzz714, zzz715, zzz716, zzz717, zzz718, Branch(zzz7190, zzz7191, zzz7192, zzz7193, zzz7194), h, ba) → new_glueBal2Mid_key10(zzz705, zzz706, zzz707, zzz708, zzz709, zzz710, zzz711, zzz712, zzz713, zzz714, zzz7190, zzz7191, zzz7192, zzz7193, zzz7194, h, ba)

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

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



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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(zzz50000), Succ(zzz40000)) → new_primEqNat(zzz50000, zzz40000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primCmpNat(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat(zzz240000, zzz22000000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primMinusNat(Succ(zzz432200), Succ(zzz55500)) → new_primMinusNat(zzz432200, zzz55500)

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
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat(Succ(zzz20100), Succ(zzz4000000)) → new_primPlusNat(zzz20100, zzz4000000)

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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primMulNat(Succ(zzz500000), Succ(zzz400000)) → new_primMulNat(zzz500000, Succ(zzz400000))

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_esEs3(Just(zzz5000), Just(zzz4000), app(app(ty_@2, bdd), bde)) → new_esEs0(zzz5000, zzz4000, bdd, bde)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(app(app(ty_@3, ec), ed), ee), dg) → new_esEs2(zzz5000, zzz4000, ec, ed, ee)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(app(app(ty_@3, bac), bad), bae), hf, hg) → new_esEs2(zzz5000, zzz4000, bac, bad, bae)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(app(ty_Either, hd), he), hf, hg) → new_esEs(zzz5000, zzz4000, hd, he)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, app(app(ty_@2, bbb), bbc), hg) → new_esEs0(zzz5001, zzz4001, bbb, bbc)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eg, app(app(app(ty_@3, ff), fg), fh)) → new_esEs2(zzz5001, zzz4001, ff, fg, fh)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, app(ty_Maybe, bbh), hg) → new_esEs3(zzz5001, zzz4001, bbh)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, hf, app(app(ty_@2, bcc), bcd)) → new_esEs0(zzz5002, zzz4002, bcc, bcd)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(ty_Maybe, dd)) → new_esEs3(zzz5000, zzz4000, dd)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(ty_[], cg)) → new_esEs1(zzz5000, zzz4000, cg)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, hf, app(ty_Maybe, bda)) → new_esEs3(zzz5002, zzz4002, bda)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hc) → new_esEs1(zzz5001, zzz4001, hc)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, app(ty_[], bbd), hg) → new_esEs1(zzz5001, zzz4001, bbd)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(app(ty_@2, hh), baa), hf, hg) → new_esEs0(zzz5000, zzz4000, hh, baa)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(ty_[], eb), dg) → new_esEs1(zzz5000, zzz4000, eb)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(ty_[], gf)) → new_esEs1(zzz5000, zzz4000, gf)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(app(ty_@2, ce), cf)) → new_esEs0(zzz5000, zzz4000, ce, cf)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(app(ty_Either, de), df), dg) → new_esEs(zzz5000, zzz4000, de, df)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eg, app(app(ty_Either, eh), fa)) → new_esEs(zzz5001, zzz4001, eh, fa)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, app(app(ty_Either, bah), bba), hg) → new_esEs(zzz5001, zzz4001, bah, bba)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, hf, app(app(ty_Either, bca), bcb)) → new_esEs(zzz5002, zzz4002, bca, bcb)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(app(ty_Either, cc), cd)) → new_esEs(zzz5000, zzz4000, cc, cd)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eg, app(ty_Maybe, ga)) → new_esEs3(zzz5001, zzz4001, ga)
new_esEs(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bc), bd), bb) → new_esEs0(zzz5000, zzz4000, bc, bd)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(ty_Maybe, ef), dg) → new_esEs3(zzz5000, zzz4000, ef)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, app(app(app(ty_@3, bbe), bbf), bbg), hg) → new_esEs2(zzz5001, zzz4001, bbe, bbf, bbg)
new_esEs3(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(zzz5000, zzz4000, bdg, bdh, bea)
new_esEs3(Just(zzz5000), Just(zzz4000), app(ty_Maybe, beb)) → new_esEs3(zzz5000, zzz4000, beb)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(ty_Maybe, baf), hf, hg) → new_esEs3(zzz5000, zzz4000, baf)
new_esEs(Left(zzz5000), Left(zzz4000), app(ty_Maybe, ca), bb) → new_esEs3(zzz5000, zzz4000, ca)
new_esEs3(Just(zzz5000), Just(zzz4000), app(app(ty_Either, bdb), bdc)) → new_esEs(zzz5000, zzz4000, bdb, bdc)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(app(ty_@2, dh), ea), dg) → new_esEs0(zzz5000, zzz4000, dh, ea)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, hf, app(ty_[], bce)) → new_esEs1(zzz5002, zzz4002, bce)
new_esEs(Left(zzz5000), Left(zzz4000), app(ty_[], be), bb) → new_esEs1(zzz5000, zzz4000, be)
new_esEs(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bf), bg), bh), bb) → new_esEs2(zzz5000, zzz4000, bf, bg, bh)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(app(app(ty_@3, da), db), dc)) → new_esEs2(zzz5000, zzz4000, da, db, dc)
new_esEs3(Just(zzz5000), Just(zzz4000), app(ty_[], bdf)) → new_esEs1(zzz5000, zzz4000, bdf)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eg, app(ty_[], fd)) → new_esEs1(zzz5001, zzz4001, fd)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(ty_[], bab), hf, hg) → new_esEs1(zzz5000, zzz4000, bab)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(app(app(ty_@3, gg), gh), ha)) → new_esEs2(zzz5000, zzz4000, gg, gh, ha)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eg, app(app(ty_@2, fb), fc)) → new_esEs0(zzz5001, zzz4001, fb, fc)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(app(ty_Either, gb), gc)) → new_esEs(zzz5000, zzz4000, gb, gc)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(ty_Maybe, hb)) → new_esEs3(zzz5000, zzz4000, hb)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(app(ty_@2, gd), ge)) → new_esEs0(zzz5000, zzz4000, gd, ge)
new_esEs(Left(zzz5000), Left(zzz4000), app(app(ty_Either, h), ba), bb) → new_esEs(zzz5000, zzz4000, h, ba)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bag, hf, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs2(zzz5002, zzz4002, bcf, bcg, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_ltEs0(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, db), dc), dd), ce) → new_ltEs2(zzz24000, zzz2200000, db, dc, dd)
new_compare20(Left(Left(zzz24000)), Left(Left(zzz2200000)), False, app(app(ty_Either, app(app(ty_@2, de), df)), ce), cc) → new_ltEs3(zzz24000, zzz2200000, de, df)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), app(ty_[], bdc), bdd) → new_lt(zzz24000, zzz2200000, bdc)
new_ltEs1(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, ff), fg), fh)) → new_ltEs2(zzz24000, zzz2200000, ff, fg, fh)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, app(app(app(ty_@3, bac), bad), bae), hg) → new_lt2(zzz24001, zzz2200001, bac, bad, bae)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), gd), app(app(ty_@2, hd), he)), cc) → new_ltEs3(zzz24002, zzz2200002, hd, he)
new_compare20(Left(:(zzz24000, zzz24001)), Left(:(zzz2200000, zzz2200001)), False, app(ty_[], h), cc) → new_compare(zzz24001, zzz2200001, h)
new_compare20(Left(Right(zzz24000)), Left(Right(zzz2200000)), False, app(app(ty_Either, dg), app(ty_[], dh)), cc) → new_ltEs(zzz24000, zzz2200000, dh)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, bca), app(ty_Maybe, bce)), cc) → new_ltEs1(zzz24001, zzz2200001, bce)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, app(ty_Maybe, bab), hg) → new_lt1(zzz24001, zzz2200001, bab)
new_primCompAux(zzz24000, zzz2200000, zzz257, app(ty_[], ba)) → new_compare(zzz24000, zzz2200000, ba)
new_ltEs1(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, fb), fc)) → new_ltEs0(zzz24000, zzz2200000, fb, fc)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), app(ty_Maybe, bbc), gd, hg) → new_compare21(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bbc), bbc)
new_lt1(zzz24000, zzz2200000, bbc) → new_compare21(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bbc), bbc)
new_compare20(Right(zzz2400), Right(zzz220000), False, cb, app(app(ty_Either, bef), beg)) → new_ltEs0(zzz2400, zzz220000, bef, beg)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, gd, app(ty_Maybe, gh)) → new_ltEs1(zzz24002, zzz2200002, gh)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), app(ty_Maybe, bdg), bdd) → new_lt1(zzz24000, zzz2200000, bdg)
new_ltEs1(Just(zzz24000), Just(zzz2200000), app(ty_[], fa)) → new_ltEs(zzz24000, zzz2200000, fa)
new_primCompAux(zzz24000, zzz2200000, zzz257, app(ty_Maybe, bd)) → new_compare2(zzz24000, zzz2200000, bd)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), bca, app(app(ty_@2, bda), bdb)) → new_ltEs3(zzz24001, zzz2200001, bda, bdb)
new_lt0(zzz240, zzz22000, cb, cc) → new_compare20(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, cb, cc), cb, cc)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), app(app(app(ty_@3, bbd), bbe), bbf), gd, hg) → new_compare22(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, bbd, bbe, bbf), bbd, bbe, bbf)
new_ltEs0(Right(zzz24000), Right(zzz2200000), dg, app(ty_[], dh)) → new_ltEs(zzz24000, zzz2200000, dh)
new_compare23(zzz24000, zzz2200000, False, bbg, bbh) → new_ltEs3(zzz24000, zzz2200000, bbg, bbh)
new_ltEs0(Right(zzz24000), Right(zzz2200000), dg, app(app(ty_Either, ea), eb)) → new_ltEs0(zzz24000, zzz2200000, ea, eb)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), app(app(ty_@2, bec), bed), bdd) → new_lt3(zzz24000, zzz2200000, bec, bed)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), app(app(ty_@2, bbg), bbh), gd, hg) → new_compare23(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bbg, bbh), bbg, bbh)
new_ltEs0(Right(zzz24000), Right(zzz2200000), dg, app(app(app(ty_@3, ed), ee), ef)) → new_ltEs2(zzz24000, zzz2200000, ed, ee, ef)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, app(ty_Maybe, bbc)), gd), hg), cc) → new_compare21(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bbc), bbc)
new_compare20(Left(Left(zzz24000)), Left(Left(zzz2200000)), False, app(app(ty_Either, app(app(ty_Either, cf), cg)), ce), cc) → new_ltEs0(zzz24000, zzz2200000, cf, cg)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), app(app(ty_@2, baf), bag)), hg), cc) → new_lt3(zzz24001, zzz2200001, baf, bag)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, gd, app(ty_[], ge)) → new_ltEs(zzz24002, zzz2200002, ge)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), gd), app(app(ty_Either, gf), gg)), cc) → new_ltEs0(zzz24002, zzz2200002, gf, gg)
new_primCompAux(zzz24000, zzz2200000, zzz257, app(app(app(ty_@3, be), bf), bg)) → new_compare3(zzz24000, zzz2200000, be, bf, bg)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), app(ty_[], bah), gd, hg) → new_compare(zzz24000, zzz2200000, bah)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, bca), app(ty_[], bcb)), cc) → new_ltEs(zzz24001, zzz2200001, bcb)
new_compare20(Left(Just(zzz24000)), Left(Just(zzz2200000)), False, app(ty_Maybe, app(app(ty_Either, fb), fc)), cc) → new_ltEs0(zzz24000, zzz2200000, fb, fc)
new_compare20(Left(Left(zzz24000)), Left(Left(zzz2200000)), False, app(app(ty_Either, app(ty_[], cd)), ce), cc) → new_ltEs(zzz24000, zzz2200000, cd)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), app(ty_[], hf)), hg), cc) → new_lt(zzz24001, zzz2200001, hf)
new_compare1(zzz240, zzz22000, cb, cc) → new_compare20(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, cb, cc), cb, cc)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, app(app(ty_@2, baf), bag), hg) → new_lt3(zzz24001, zzz2200001, baf, bag)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, app(app(ty_Either, hh), baa), hg) → new_lt0(zzz24001, zzz2200001, hh, baa)
new_compare22(zzz24000, zzz2200000, False, bbd, bbe, bbf) → new_ltEs2(zzz24000, zzz2200000, bbd, bbe, bbf)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, bca), app(app(app(ty_@3, bcf), bcg), bch)), cc) → new_ltEs2(zzz24001, zzz2200001, bcf, bcg, bch)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bbd), bbe), bbf)), gd), hg), cc) → new_compare22(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, bbd, bbe, bbf), bbd, bbe, bbf)
new_compare20(Left(Right(zzz24000)), Left(Right(zzz2200000)), False, app(app(ty_Either, dg), app(app(app(ty_@3, ed), ee), ef)), cc) → new_ltEs2(zzz24000, zzz2200000, ed, ee, ef)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, gd, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs2(zzz24002, zzz2200002, ha, hb, hc)
new_ltEs(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), h) → new_compare(zzz24001, zzz2200001, h)
new_ltEs(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), h) → new_primCompAux(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, h), h)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, app(ty_[], bdc)), bdd), cc) → new_lt(zzz24000, zzz2200000, bdc)
new_compare20(Left(Just(zzz24000)), Left(Just(zzz2200000)), False, app(ty_Maybe, app(ty_Maybe, fd)), cc) → new_ltEs1(zzz24000, zzz2200000, fd)
new_compare20(Left(:(zzz24000, zzz24001)), Left(:(zzz2200000, zzz2200001)), False, app(ty_[], h), cc) → new_primCompAux(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, h), h)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), app(app(ty_Either, hh), baa)), hg), cc) → new_lt0(zzz24001, zzz2200001, hh, baa)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, app(app(ty_Either, bde), bdf)), bdd), cc) → new_lt0(zzz24000, zzz2200000, bde, bdf)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, app(app(ty_Either, bba), bbb)), gd), hg), cc) → new_lt0(zzz24000, zzz2200000, bba, bbb)
new_ltEs1(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, fd)) → new_ltEs1(zzz24000, zzz2200000, fd)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), app(app(ty_Either, bde), bdf), bdd) → new_lt0(zzz24000, zzz2200000, bde, bdf)
new_ltEs0(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cf), cg), ce) → new_ltEs0(zzz24000, zzz2200000, cf, cg)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), bca, app(app(ty_Either, bcc), bcd)) → new_ltEs0(zzz24001, zzz2200001, bcc, bcd)
new_compare3(zzz24000, zzz2200000, bbd, bbe, bbf) → new_compare22(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, bbd, bbe, bbf), bbd, bbe, bbf)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, app(ty_[], bah)), gd), hg), cc) → new_compare(zzz24000, zzz2200000, bah)
new_compare20(Left(Left(zzz24000)), Left(Left(zzz2200000)), False, app(app(ty_Either, app(ty_Maybe, da)), ce), cc) → new_ltEs1(zzz24000, zzz2200000, da)
new_compare20(Right(zzz2400), Right(zzz220000), False, cb, app(app(ty_@2, bfd), bfe)) → new_ltEs3(zzz2400, zzz220000, bfd, bfe)
new_lt3(zzz24000, zzz2200000, bbg, bbh) → new_compare23(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bbg, bbh), bbg, bbh)
new_lt(zzz24000, zzz2200000, bah) → new_compare(zzz24000, zzz2200000, bah)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, bca), app(app(ty_Either, bcc), bcd)), cc) → new_ltEs0(zzz24001, zzz2200001, bcc, bcd)
new_ltEs0(Left(zzz24000), Left(zzz2200000), app(ty_[], cd), ce) → new_ltEs(zzz24000, zzz2200000, cd)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, app(ty_[], hf), hg) → new_lt(zzz24001, zzz2200001, hf)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, bca), app(app(ty_@2, bda), bdb)), cc) → new_ltEs3(zzz24001, zzz2200001, bda, bdb)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, app(app(ty_@2, bec), bed)), bdd), cc) → new_lt3(zzz24000, zzz2200000, bec, bed)
new_compare20(Left(Right(zzz24000)), Left(Right(zzz2200000)), False, app(app(ty_Either, dg), app(ty_Maybe, ec)), cc) → new_ltEs1(zzz24000, zzz2200000, ec)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, gd, app(app(ty_@2, hd), he)) → new_ltEs3(zzz24002, zzz2200002, hd, he)
new_primCompAux(zzz24000, zzz2200000, zzz257, app(app(ty_Either, bb), bc)) → new_compare1(zzz24000, zzz2200000, bb, bc)
new_compare20(Left(Just(zzz24000)), Left(Just(zzz2200000)), False, app(ty_Maybe, app(app(ty_@2, ga), gb)), cc) → new_ltEs3(zzz24000, zzz2200000, ga, gb)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), app(app(app(ty_@3, bac), bad), bae)), hg), cc) → new_lt2(zzz24001, zzz2200001, bac, bad, bae)
new_compare20(Left(Right(zzz24000)), Left(Right(zzz2200000)), False, app(app(ty_Either, dg), app(app(ty_Either, ea), eb)), cc) → new_ltEs0(zzz24000, zzz2200000, ea, eb)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), gd), app(ty_Maybe, gh)), cc) → new_ltEs1(zzz24002, zzz2200002, gh)
new_compare20(Left(Right(zzz24000)), Left(Right(zzz2200000)), False, app(app(ty_Either, dg), app(app(ty_@2, eg), eh)), cc) → new_ltEs3(zzz24000, zzz2200000, eg, eh)
new_lt2(zzz24000, zzz2200000, bbd, bbe, bbf) → new_compare22(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, bbd, bbe, bbf), bbd, bbe, bbf)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), bca, app(app(app(ty_@3, bcf), bcg), bch)) → new_ltEs2(zzz24001, zzz2200001, bcf, bcg, bch)
new_compare20(Left(Left(zzz24000)), Left(Left(zzz2200000)), False, app(app(ty_Either, app(app(app(ty_@3, db), dc), dd)), ce), cc) → new_ltEs2(zzz24000, zzz2200000, db, dc, dd)
new_compare20(Left(Just(zzz24000)), Left(Just(zzz2200000)), False, app(ty_Maybe, app(app(app(ty_@3, ff), fg), fh)), cc) → new_ltEs2(zzz24000, zzz2200000, ff, fg, fh)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, app(app(app(ty_@3, bdh), bea), beb)), bdd), cc) → new_lt2(zzz24000, zzz2200000, bdh, bea, beb)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), app(app(app(ty_@3, bdh), bea), beb), bdd) → new_lt2(zzz24000, zzz2200000, bdh, bea, beb)
new_ltEs0(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, de), df), ce) → new_ltEs3(zzz24000, zzz2200000, de, df)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), app(app(ty_Either, bba), bbb), gd, hg) → new_lt0(zzz24000, zzz2200000, bba, bbb)
new_compare20(Left(Just(zzz24000)), Left(Just(zzz2200000)), False, app(ty_Maybe, app(ty_[], fa)), cc) → new_ltEs(zzz24000, zzz2200000, fa)
new_compare(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), h) → new_compare(zzz24001, zzz2200001, h)
new_compare20(Right(zzz2400), Right(zzz220000), False, cb, app(ty_Maybe, beh)) → new_ltEs1(zzz2400, zzz220000, beh)
new_compare(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), h) → new_primCompAux(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, h), h)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), gd), app(ty_[], ge)), cc) → new_ltEs(zzz24002, zzz2200002, ge)
new_primCompAux(zzz24000, zzz2200000, zzz257, app(app(ty_@2, bh), ca)) → new_compare4(zzz24000, zzz2200000, bh, ca)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), app(ty_Maybe, bab)), hg), cc) → new_lt1(zzz24001, zzz2200001, bab)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), bca, app(ty_Maybe, bce)) → new_ltEs1(zzz24001, zzz2200001, bce)
new_ltEs2(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, gd, app(app(ty_Either, gf), gg)) → new_ltEs0(zzz24002, zzz2200002, gf, gg)
new_compare20(Left(@2(zzz24000, zzz24001)), Left(@2(zzz2200000, zzz2200001)), False, app(app(ty_@2, app(ty_Maybe, bdg)), bdd), cc) → new_lt1(zzz24000, zzz2200000, bdg)
new_ltEs3(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), bca, app(ty_[], bcb)) → new_ltEs(zzz24001, zzz2200001, bcb)
new_compare2(zzz24000, zzz2200000, bbc) → new_compare21(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bbc), bbc)
new_ltEs0(Right(zzz24000), Right(zzz2200000), dg, app(app(ty_@2, eg), eh)) → new_ltEs3(zzz24000, zzz2200000, eg, eh)
new_ltEs1(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, ga), gb)) → new_ltEs3(zzz24000, zzz2200000, ga, gb)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, app(app(ty_@2, bbg), bbh)), gd), hg), cc) → new_compare23(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bbg, bbh), bbg, bbh)
new_compare4(zzz24000, zzz2200000, bbg, bbh) → new_compare23(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bbg, bbh), bbg, bbh)
new_ltEs0(Right(zzz24000), Right(zzz2200000), dg, app(ty_Maybe, ec)) → new_ltEs1(zzz24000, zzz2200000, ec)
new_compare20(Left(@3(zzz24000, zzz24001, zzz24002)), Left(@3(zzz2200000, zzz2200001, zzz2200002)), False, app(app(app(ty_@3, gc), gd), app(app(app(ty_@3, ha), hb), hc)), cc) → new_ltEs2(zzz24002, zzz2200002, ha, hb, hc)
new_compare20(Right(zzz2400), Right(zzz220000), False, cb, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs2(zzz2400, zzz220000, bfa, bfb, bfc)
new_compare21(zzz24000, zzz2200000, False, bbc) → new_ltEs1(zzz24000, zzz2200000, bbc)
new_ltEs0(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, da), ce) → new_ltEs1(zzz24000, zzz2200000, da)
new_compare20(Right(zzz2400), Right(zzz220000), False, cb, app(ty_[], bee)) → new_ltEs(zzz2400, zzz220000, bee)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, cb, cc) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, cc), cb, cc)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], bee)) → new_ltEs12(zzz2400, zzz220000, bee)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, ddf, ddg) → LT
new_lt18(zzz24000, zzz2200000, bbd, bbe, bbf) → new_esEs8(new_compare26(zzz24000, zzz2200000, bbd, bbe, bbf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(zzz5000, zzz4000, dbf, dbg, dbh)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, bh), ca)) → new_compare5(zzz24000, zzz2200000, bh, ca)
new_compare211(Left(zzz2400), Left(zzz220000), False, cb, cc) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, cb), cb, cc)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, app(ty_Maybe, dcb)) → new_esEs5(zzz5000, zzz4000, dcb)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, chb)) → new_ltEs5(zzz24001, zzz2200001, chb)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, cge)) → new_ltEs5(zzz24002, zzz2200002, cge)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, dg), ce)) → new_ltEs16(zzz2400, zzz220000, dg, ce)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, cba), cbb)) → new_esEs7(zzz5002, zzz4002, cba, cbb)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, baf), bag)) → new_lt4(zzz24001, zzz2200001, baf, bag)
new_primCompAux0(zzz24000, zzz2200000, zzz257, h) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, h))
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], fa)) → new_ltEs12(zzz24000, zzz2200000, fa)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bbc)) → new_lt17(zzz24000, zzz2200000, bbc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, ce) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, bdh), bea), beb)) → new_lt18(zzz24000, zzz2200000, bdh, bea, beb)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], bdc)) → new_lt6(zzz24000, zzz2200000, bdc)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ddd)) → new_esEs20(zzz5000, zzz4000, ddd)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), cfa) → new_asAs(new_esEs23(zzz5000, zzz4000, cfa), new_esEs18(zzz5001, zzz4001, cfa))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, cgg)) → new_ltEs5(zzz24000, zzz2200000, cgg)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, che) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, ce) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, cca) → new_esEs8(new_compare9(zzz24000, zzz2200000, cca), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), h) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, h), h)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dde)) → new_esEs5(zzz5000, zzz4000, dde)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, ff), fg), fh)) → new_ltEs10(zzz24000, zzz2200000, ff, fg, fh)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], ge)) → new_ltEs12(zzz24002, zzz2200002, ge)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, cbg)) → new_esEs20(zzz5002, zzz4002, cbg)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, app(ty_[], dh)) → new_ltEs12(zzz24000, zzz2200000, dh)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, dea)) → new_compare9(zzz24000, zzz2200000, dea)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), bca, bdd) → new_pePe(new_lt20(zzz24000, zzz2200000, bca), new_asAs(new_esEs28(zzz24000, zzz2200000, bca), new_ltEs19(zzz24001, zzz2200001, bdd)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, che) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bbg, bbh) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bbg, bbh), bbg, bbh)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], bgg)) → new_esEs18(zzz5000, zzz4000, bgg)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, cae)) → new_esEs20(zzz5001, zzz4001, cae)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, baf), bag)) → new_esEs7(zzz24001, zzz2200001, baf, bag)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, hh), baa)) → new_esEs4(zzz24001, zzz2200001, hh, baa)
new_esEs18(:(zzz5000, zzz5001), [], cfa) → False
new_esEs18([], :(zzz4000, zzz4001), cfa) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, cdf), cdg)) → new_esEs4(zzz5001, zzz4001, cdf, cdg)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, cgf) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, cgf)) → new_ltEs17(zzz2400, zzz220000, cgf)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, da), ce) → new_ltEs17(zzz24000, zzz2200000, da)
new_compare10(zzz24000, zzz2200000, True, bbc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], h)) → new_ltEs12(zzz2400, zzz220000, h)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, bca), bdd)) → new_ltEs7(zzz2400, zzz220000, bca, bdd)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, app(app(ty_@2, dbc), dbd)) → new_esEs7(zzz5000, zzz4000, dbc, dbd)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs6(zzz5002, zzz4002, cbd, cbe, cbf)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cha)) → new_lt9(zzz24000, zzz2200000, cha)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bbc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, bhe), bhf)) → new_esEs4(zzz5001, zzz4001, bhe, bhf)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], h) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, app(app(ty_@2, eg), eh)) → new_ltEs7(zzz24000, zzz2200000, eg, eh)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], hf)) → new_esEs18(zzz24001, zzz2200001, hf)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, beh)) → new_ltEs17(zzz2400, zzz220000, beh)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bah)) → new_esEs18(zzz24000, zzz2200000, bah)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, cdh), cea)) → new_esEs7(zzz5001, zzz4001, cdh, cea)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bbc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bbc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, ddf, ddg) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, fb), fc)) → new_ltEs16(zzz24000, zzz2200000, fb, fc)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, bbd, bbe, bbf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, daf), che) → new_esEs20(zzz5000, zzz4000, daf)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bbg), bbh)) → new_esEs7(zzz24000, zzz2200000, bbg, bbh)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], ceb)) → new_esEs18(zzz5001, zzz4001, ceb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, ce) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bbc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bbc), bbc)
new_compare17(zzz24000, zzz2200000, True, bbg, bbh) → LT
new_compare29(zzz24000, zzz2200000, True, bbd, bbe, bbf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), dah, app(app(ty_Either, dba), dbb)) → new_esEs4(zzz5000, zzz4000, dba, dbb)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, cgb)) → new_esEs20(zzz5000, zzz4000, cgb)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(zzz5001, zzz4001, cec, ced, cee)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, chf), chg), che) → new_esEs4(zzz5000, zzz4000, chf, chg)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, app(ty_Ratio, dca)) → new_esEs20(zzz5000, zzz4000, dca)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], caa)) → new_esEs18(zzz5001, zzz4001, caa)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, che) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bab)) → new_lt17(zzz24001, zzz2200001, bab)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, che) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], cch)) → new_esEs18(zzz5000, zzz4000, cch)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cgh) → new_asAs(new_esEs26(zzz5000, zzz4000, cgh), new_esEs27(zzz5001, zzz4001, cgh))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs6(zzz24000, zzz2200000, bbd, bbe, bbf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, ccf), ccg)) → new_esEs7(zzz5000, zzz4000, ccf, ccg)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, ccd), cce)) → new_esEs4(zzz5000, zzz4000, ccd, cce)
new_compare24(zzz24000, zzz2200000, True, bbg, bbh) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, app(app(ty_Either, ea), eb)) → new_ltEs16(zzz24000, zzz2200000, ea, eb)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, ceh)) → new_ltEs5(zzz2400, zzz220000, ceh)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, cef)) → new_esEs20(zzz5001, zzz4001, cef)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, cdd)) → new_esEs20(zzz5000, zzz4000, cdd)
new_compare32(zzz24000, zzz2200000, app(ty_[], ba)) → new_compare0(zzz24000, zzz2200000, ba)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bba), bbb)) → new_lt11(zzz24000, zzz2200000, bba, bbb)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, bec), bed)) → new_esEs7(zzz24000, zzz2200000, bec, bed)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, ce) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, ce) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, che) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bab)) → new_esEs5(zzz24001, zzz2200001, bab)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, bge), bgf)) → new_esEs7(zzz5000, zzz4000, bge, bgf)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, che) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddh)) → new_ltEs5(zzz2400, zzz220000, ddh)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), gc, gd, hg) → new_pePe(new_lt13(zzz24000, zzz2200000, gc), new_asAs(new_esEs24(zzz24000, zzz2200000, gc), new_pePe(new_lt12(zzz24001, zzz2200001, gd), new_asAs(new_esEs25(zzz24001, zzz2200001, gd), new_ltEs11(zzz24002, zzz2200002, hg)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, bhg), bhh)) → new_esEs7(zzz5001, zzz4001, bhg, bhh)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, ce) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], cbc)) → new_esEs18(zzz5002, zzz4002, cbc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, app(app(app(ty_@3, ed), ee), ef)) → new_ltEs10(zzz24000, zzz2200000, ed, ee, ef)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, bec), bed)) → new_lt4(zzz24000, zzz2200000, bec, bed)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bff, bfg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, bbd, bbe, bbf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, bbd, bbe, bbf), bbd, bbe, bbf)
new_lt6(zzz24000, zzz2200000, bah) → new_esEs8(new_compare0(zzz24000, zzz2200000, bah), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, app(ty_Maybe, ec)) → new_ltEs17(zzz24000, zzz2200000, ec)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bbc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, cgd)) → new_lt9(zzz24001, zzz2200001, cgd)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, h) → new_fsEs(new_compare0(zzz2400, zzz220000, h))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, de), df), ce) → new_ltEs7(zzz24000, zzz2200000, de, df)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bbg, bbh) → new_esEs8(new_compare5(zzz24000, zzz2200000, bbg, bbh), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bbg, bbh) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), ccb, ccc) → new_asAs(new_esEs21(zzz5000, zzz4000, ccb), new_esEs22(zzz5001, zzz4001, ccc))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, bgc), bgd)) → new_esEs4(zzz5000, zzz4000, bgc, bgd)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, bbd, bbe, bbf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, app(ty_[], dbe)) → new_esEs18(zzz5000, zzz4000, dbe)
new_ltEs16(Left(zzz24000), Right(zzz2200000), dg, ce) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], bcb)) → new_ltEs12(zzz24001, zzz2200001, bcb)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, ce) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, bhd)) → new_esEs5(zzz5000, zzz4000, bhd)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, bdg)) → new_lt17(zzz24000, zzz2200000, bdg)
new_compare0(:(zzz24000, zzz24001), [], h) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, che) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, be), bf), bg)) → new_compare26(zzz24000, zzz2200000, be, bf, bg)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bbc)) → new_esEs5(zzz24000, zzz2200000, bbc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, cca)) → new_lt9(zzz24000, zzz2200000, cca)
new_compare11(zzz235, zzz236, False, bff, bfg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, cbh)) → new_esEs5(zzz5002, zzz4002, cbh)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, bac), bad), bae)) → new_lt18(zzz24001, zzz2200001, bac, bad, bae)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs10(zzz24002, zzz2200002, ha, hb, hc)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, cfb), cfc)) → new_esEs4(zzz5000, zzz4000, cfb, cfc)
new_ltEs17(Nothing, Just(zzz2200000), cgf) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs6(zzz24000, zzz2200000, bdh, bea, beb)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bba), bbb)) → new_esEs4(zzz24000, zzz2200000, bba, bbb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, bfd), bfe)) → new_ltEs7(zzz2400, zzz220000, bfd, bfe)
new_compare31(zzz24000, zzz2200000, bbc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bbc), bbc)
new_ltEs17(Nothing, Nothing, cgf) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, bde), bdf)) → new_lt11(zzz24000, zzz2200000, bde, bdf)
new_lt13(zzz24000, zzz2200000, app(ty_[], bah)) → new_lt6(zzz24000, zzz2200000, bah)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, hh), baa)) → new_lt11(zzz24001, zzz2200001, hh, baa)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, bce)) → new_ltEs17(zzz24001, zzz2200001, bce)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cd), ce) → new_ltEs12(zzz24000, zzz2200000, cd)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, caf)) → new_esEs5(zzz5001, zzz4001, caf)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dda), ddb), ddc)) → new_esEs6(zzz5000, zzz4000, dda, ddb, ddc)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bbg), bbh)) → new_lt4(zzz24000, zzz2200000, bbg, bbh)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], bdc)) → new_esEs18(zzz24000, zzz2200000, bdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, bbd, bbe, bbf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, bbd, bbe, bbf), bbd, bbe, bbf)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, bda), bdb)) → new_ltEs7(zzz24001, zzz2200001, bda, bdb)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, cab), cac), cad)) → new_esEs6(zzz5001, zzz4001, cab, cac, cad)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, bd)) → new_compare31(zzz24000, zzz2200000, bd)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, cag), cah)) → new_esEs4(zzz5002, zzz4002, cag, cah)
new_esEs18([], [], cfa) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, cfg), cfh), cga)) → new_esEs6(zzz5000, zzz4000, cfg, cfh, cga)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, bb), bc)) → new_compare19(zzz24000, zzz2200000, bb, bc)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, cfd), cfe)) → new_esEs7(zzz5000, zzz4000, cfd, cfe)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, dag), che) → new_esEs5(zzz5000, zzz4000, dag)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, bde), bdf)) → new_esEs4(zzz24000, zzz2200000, bde, bdf)
new_compare211(Right(zzz2400), Left(zzz220000), False, cb, cc) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, cgc)) → new_esEs5(zzz5000, zzz4000, cgc)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs6(zzz24001, zzz2200001, bac, bad, bae)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], dab), che) → new_esEs18(zzz5000, zzz4000, dab)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, cb, cc) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, hd), he)) → new_ltEs7(zzz24002, zzz2200002, hd, he)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), dcc) → False
new_esEs5(Just(zzz5000), Nothing, dcc) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), dg, ce) → False
new_compare211(zzz240, zzz22000, True, cb, cc) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, chh), daa), che) → new_esEs7(zzz5000, zzz4000, chh, daa)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cha)) → new_esEs20(zzz24000, zzz2200000, cha)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, app(ty_Ratio, chd)) → new_ltEs5(zzz24000, zzz2200000, chd)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dg, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, ce) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, ga), gb)) → new_ltEs7(zzz24000, zzz2200000, ga, gb)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, dcc) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, bdg)) → new_esEs5(zzz24000, zzz2200000, bdg)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), dah, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, gf), gg)) → new_ltEs16(zzz24002, zzz2200002, gf, gg)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, bhc)) → new_esEs20(zzz5000, zzz4000, bhc)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs10(zzz2400, zzz220000, bfa, bfb, bfc)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bbg, bbh) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bbg, bbh), bbg, bbh)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, fd)) → new_ltEs17(zzz24000, zzz2200000, fd)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, ceg)) → new_esEs5(zzz5001, zzz4001, ceg)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, cde)) → new_esEs5(zzz5000, zzz4000, cde)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs6(zzz5000, zzz4000, bgh, bha, bhb)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), h) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, cda), cdb), cdc)) → new_esEs6(zzz5000, zzz4000, cda, cdb, cdc)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), dah, che) → False
new_esEs4(Left(zzz5000), Right(zzz4000), dah, che) → False
new_lt11(zzz240, zzz22000, cb, cc) → new_esEs8(new_compare19(zzz240, zzz22000, cb, cc), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dcf), dcg)) → new_esEs7(zzz5000, zzz4000, dcf, dcg)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, dac), dad), dae), che) → new_esEs6(zzz5000, zzz4000, dac, dad, dae)
new_lt12(zzz24001, zzz2200001, app(ty_[], hf)) → new_lt6(zzz24001, zzz2200001, hf)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, cb, cc) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, cb, cc), cb, cc)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cf), cg), ce) → new_ltEs16(zzz24000, zzz2200000, cf, cg)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, cca)) → new_esEs20(zzz24000, zzz2200000, cca)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, gc), gd), hg)) → new_ltEs10(zzz2400, zzz220000, gc, gd, hg)
new_ltEs5(zzz2400, zzz220000, ceh) → new_fsEs(new_compare9(zzz2400, zzz220000, ceh))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, bbd), bbe), bbf)) → new_lt18(zzz24000, zzz2200000, bbd, bbe, bbf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, bcf), bcg), bch)) → new_ltEs10(zzz24001, zzz2200001, bcf, bcg, bch)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), bfh, bga, bgb) → new_asAs(new_esEs9(zzz5000, zzz4000, bfh), new_asAs(new_esEs10(zzz5001, zzz4001, bga), new_esEs11(zzz5002, zzz4002, bgb)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, che) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, gh)) → new_ltEs17(zzz24002, zzz2200002, gh)
new_esEs23(zzz5000, zzz4000, app(ty_[], cff)) → new_esEs18(zzz5000, zzz4000, cff)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, chc), ce) → new_ltEs5(zzz24000, zzz2200000, chc)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, bcc), bcd)) → new_ltEs16(zzz24001, zzz2200001, bcc, bcd)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dch)) → new_esEs18(zzz5000, zzz4000, dch)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, bef), beg)) → new_ltEs16(zzz2400, zzz220000, bef, beg)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dcd), dce)) → new_esEs4(zzz5000, zzz4000, dcd, dce)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, db), dc), dd), ce) → new_ltEs10(zzz24000, zzz2200000, db, dc, dd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, cgd)) → new_esEs20(zzz24001, zzz2200001, cgd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_sr(x0, x1)
new_lt6(x0, x1, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs22(x0, x1, ty_Double)
new_ltEs8(EQ, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_compare0([], [], x0)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare5(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(x0, x1)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_ltEs14(True, False)
new_ltEs14(False, True)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_esEs8(GT, GT)
new_esEs18([], :(x0, x1), x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(LT, LT)
new_esEs24(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs16(True, False)
new_esEs16(False, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, True)
new_compare32(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare32(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Int)
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt12(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs15(Char(x0), Char(x1))
new_compare0(:(x0, x1), [], x2)
new_lt15(x0, x1)
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_lt14(x0, x1)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Ordering)
new_compare32(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_@0)
new_lt18(x0, x1, x2, x3, x4)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs12(x0, x1, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_compare25(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Float)
new_ltEs17(Nothing, Nothing, x0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Zero)
new_compare24(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs5(x0, x1, x2)
new_esEs10(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Double)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_ltEs17(Just(x0), Nothing, x1)
new_sr0(Integer(x0), Integer(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Nothing, x0)
new_lt12(x0, x1, ty_Float)
new_primCompAux0(x0, x1, x2, x3)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt10(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare11(x0, x1, False, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs10(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare211(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare19(x0, x1, x2, x3)
new_lt19(x0, x1)
new_ltEs13(x0, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(x0, x1, ty_Int)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_ltEs21(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare26(x0, x1, x2, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(@0, @0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_compare29(x0, x1, False, x2, x3, x4)
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Zero, Zero)
new_esEs9(x0, x1, ty_Double)
new_compare11(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2, x3)
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare0([], :(x0, x1), x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_lt13(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_esEs11(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs6(x0, x1)
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs19(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, x2, x3)
new_not(True)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs5(Nothing, Just(x0), x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primPlusNat1(Succ(x0), x1)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_compare17(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Char)
new_compare32(x0, x1, ty_Bool)
new_compare24(x0, x1, False, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs17(Nothing, Just(x0), x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs18([], [], x0)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2)
new_esEs5(Just(x0), Nothing, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, x0)
new_compare12(x0, x1, False, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt12(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare32(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Char)
new_lt17(x0, x1, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Char)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(x0, x1, ty_Float)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_lt13(x0, x1, ty_Double)
new_esEs18(:(x0, x1), [], x2)
new_compare7(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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

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



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

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

new_intersectFM_C2Elt102(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz657, zzz658, zzz659, zzz660, zzz661, False, h, ba, bb) → new_intersectFM_C2Elt10(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz657, zzz658, zzz659, zzz660, zzz661, new_gt(Right(zzz656), zzz657, ba, bb), h, ba, bb)
new_intersectFM_C2Elt10(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz657, zzz658, zzz659, zzz660, zzz661, True, h, ba, bb) → new_intersectFM_C2Elt100(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz661, h, ba, bb)
new_intersectFM_C2Elt101(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz657, zzz658, zzz659, zzz660, zzz661, h, ba, bb) → new_intersectFM_C2Elt102(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz657, zzz658, zzz659, zzz660, zzz661, new_lt11(Right(zzz656), zzz657, ba, bb), h, ba, bb)
new_intersectFM_C2Elt100(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, Branch(zzz6600, zzz6601, zzz6602, zzz6603, zzz6604), h, ba, bb) → new_intersectFM_C2Elt101(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz6600, zzz6601, zzz6602, zzz6603, zzz6604, h, ba, bb)
new_intersectFM_C2Elt102(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz657, zzz658, zzz659, Branch(zzz6600, zzz6601, zzz6602, zzz6603, zzz6604), zzz661, True, h, ba, bb) → new_intersectFM_C2Elt101(zzz651, zzz652, zzz653, zzz654, zzz655, zzz656, zzz6600, zzz6601, zzz6602, zzz6603, zzz6604, h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdd, bde) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bde), bdd, bde)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dcc)) → new_ltEs12(zzz2400, zzz220000, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dca, dcb) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(zzz5000, zzz4000, daa, dab, dac)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, ded), dee)) → new_compare5(zzz24000, zzz2200000, ded, dee)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdd, bde) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdd), bdd, bde)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Maybe, dae)) → new_esEs5(zzz5000, zzz4000, dae)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, cch)) → new_ltEs5(zzz24001, zzz2200001, cch)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgf)) → new_ltEs5(zzz24002, zzz2200002, bgf)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cee), cdc)) → new_ltEs16(zzz2400, zzz220000, cee, cdc)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_lt4(zzz24001, zzz2200001, bfb, bfc)
new_primCompAux0(zzz24000, zzz2200000, zzz257, cda) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, cda))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgh)) → new_ltEs12(zzz24000, zzz2200000, bgh)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cdc) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt18(zzz24000, zzz2200000, cba, cbb, cbc)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cae)) → new_lt6(zzz24000, zzz2200000, cae)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbg)) → new_esEs20(zzz5000, zzz4000, dbg)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bca) → new_asAs(new_esEs23(zzz5000, zzz4000, bca), new_esEs18(zzz5001, zzz4001, bca))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, caa)) → new_ltEs5(zzz24000, zzz2200000, caa)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cfh) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cdc) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, ha) → new_esEs8(new_compare9(zzz24000, zzz2200000, ha), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), cda) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, cda), cda)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbh)) → new_esEs5(zzz5000, zzz4000, dbh)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_ltEs10(zzz24000, zzz2200000, bhd, bhe, bhf)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfe)) → new_ltEs12(zzz24002, zzz2200002, bfe)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_[], cef)) → new_ltEs12(zzz24000, zzz2200000, cef)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, def)) → new_compare9(zzz24000, zzz2200000, def)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), cac, cad) → new_pePe(new_lt20(zzz24000, zzz2200000, cac), new_asAs(new_esEs28(zzz24000, zzz2200000, cac), new_ltEs19(zzz24001, zzz2200001, cad)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cfh) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_esEs7(zzz24001, zzz2200001, bfb, bfc)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_esEs4(zzz24001, zzz2200001, bed, bee)
new_esEs18(:(zzz5000, zzz5001), [], bca) → False
new_esEs18([], :(zzz4000, zzz4001), bca) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, baf), bag)) → new_esEs4(zzz5001, zzz4001, baf, bag)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bgg) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bgg)) → new_ltEs17(zzz2400, zzz220000, bgg)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdf), cdc) → new_ltEs17(zzz24000, zzz2200000, cdf)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], cda)) → new_ltEs12(zzz2400, zzz220000, cda)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, cac), cad)) → new_ltEs7(zzz2400, zzz220000, cac, cad)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_@2, chf), chg)) → new_esEs7(zzz5000, zzz4000, chf, chg)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_lt9(zzz24000, zzz2200000, cbf)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], cda) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_@2, cfe), cff)) → new_ltEs7(zzz24000, zzz2200000, cfe, cff)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bec)) → new_esEs18(zzz24001, zzz2200001, bec)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcf)) → new_ltEs17(zzz2400, zzz220000, dcf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, bah), bba)) → new_esEs7(zzz5001, zzz4001, bah, bba)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dca, dcb) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bha), bhb)) → new_ltEs16(zzz24000, zzz2200000, bha, bhb)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cha), cfh) → new_esEs20(zzz5000, zzz4000, cha)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bbb)) → new_esEs18(zzz5001, zzz4001, bbb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cdc) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_Either, chd), che)) → new_esEs4(zzz5000, zzz4000, chd, che)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bdb)) → new_esEs20(zzz5000, zzz4000, bdb)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(zzz5001, zzz4001, bbc, bbd, bbe)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cga), cgb), cfh) → new_esEs4(zzz5000, zzz4000, cga, cgb)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Ratio, dad)) → new_esEs20(zzz5000, zzz4000, dad)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cfh) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_lt17(zzz24001, zzz2200001, bef)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cfh) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hh)) → new_esEs18(zzz5000, zzz4000, hh)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cab) → new_asAs(new_esEs26(zzz5000, zzz4000, cab), new_esEs27(zzz5001, zzz4001, cab))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hf), hg)) → new_esEs7(zzz5000, zzz4000, hf, hg)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hd), he)) → new_esEs4(zzz5000, zzz4000, hd, he)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_Either, ceg), ceh)) → new_ltEs16(zzz24000, zzz2200000, ceg, ceh)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbh)) → new_ltEs5(zzz2400, zzz220000, bbh)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbf)) → new_esEs20(zzz5001, zzz4001, bbf)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bad)) → new_esEs20(zzz5000, zzz4000, bad)
new_compare32(zzz24000, zzz2200000, app(ty_[], dde)) → new_compare0(zzz24000, zzz2200000, dde)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_lt11(zzz24000, zzz2200000, bea, beb)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_esEs7(zzz24000, zzz2200000, cbd, cbe)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cdc) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cdc) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cfh) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_esEs5(zzz24001, zzz2200001, bef)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cfh) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddd)) → new_ltEs5(zzz2400, zzz220000, ddd)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdf, bdg, bdh) → new_pePe(new_lt13(zzz24000, zzz2200000, bdf), new_asAs(new_esEs24(zzz24000, zzz2200000, bdf), new_pePe(new_lt12(zzz24001, zzz2200001, bdg), new_asAs(new_esEs25(zzz24001, zzz2200001, bdg), new_ltEs11(zzz24002, zzz2200002, bdh)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cdc) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs10(zzz24000, zzz2200000, cfb, cfc, cfd)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_lt4(zzz24000, zzz2200000, cbd, cbe)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Maybe, cfa)) → new_ltEs17(zzz24000, zzz2200000, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_lt9(zzz24001, zzz2200001, bfd)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, cda) → new_fsEs(new_compare0(zzz2400, zzz220000, cda))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, ceb), cec), cdc) → new_ltEs7(zzz24000, zzz2200000, ceb, cec)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), hb, hc) → new_asAs(new_esEs21(zzz5000, zzz4000, hb), new_esEs22(zzz5001, zzz4001, hc))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_[], chh)) → new_esEs18(zzz5000, zzz4000, chh)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cee, cdc) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbg)) → new_ltEs12(zzz24001, zzz2200001, cbg)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cdc) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_lt17(zzz24000, zzz2200000, cah)
new_compare0(:(zzz24000, zzz24001), [], cda) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cfh) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, dea), deb), dec)) → new_compare26(zzz24000, zzz2200000, dea, deb, dec)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_lt9(zzz24000, zzz2200000, ha)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_lt18(zzz24001, zzz2200001, beg, beh, bfa)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bga), bgb), bgc)) → new_ltEs10(zzz24002, zzz2200002, bga, bgb, bgc)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bcb), bcc)) → new_esEs4(zzz5000, zzz4000, bcb, bcc)
new_ltEs17(Nothing, Just(zzz2200000), bgg) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(zzz24000, zzz2200000, cba, cbb, cbc)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_esEs4(zzz24000, zzz2200000, bea, beb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, ddb), ddc)) → new_ltEs7(zzz2400, zzz220000, ddb, ddc)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bgg) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_lt11(zzz24000, zzz2200000, caf, cag)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_lt11(zzz24001, zzz2200001, bed, bee)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, ccb)) → new_ltEs17(zzz24001, zzz2200001, ccb)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cdb), cdc) → new_ltEs12(zzz24000, zzz2200000, cdb)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs6(zzz5000, zzz4000, dbd, dbe, dbf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cae)) → new_esEs18(zzz24000, zzz2200000, cae)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccf), ccg)) → new_ltEs7(zzz24001, zzz2200001, ccf, ccg)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_gt(zzz3510, zzz4870, gg, gh) → new_esEs8(new_compare19(zzz3510, zzz4870, gg, gh), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddh)) → new_compare31(zzz24000, zzz2200000, ddh)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bca) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zzz5000, zzz4000, bcg, bch, bda)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddf), ddg)) → new_compare19(zzz24000, zzz2200000, ddf, ddg)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcd), bce)) → new_esEs7(zzz5000, zzz4000, bcd, bce)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, chb), cfh) → new_esEs5(zzz5000, zzz4000, chb)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_esEs4(zzz24000, zzz2200000, caf, cag)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdd, bde) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bdc)) → new_esEs5(zzz5000, zzz4000, bdc)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zzz24001, zzz2200001, beg, beh, bfa)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cge), cfh) → new_esEs18(zzz5000, zzz4000, cge)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdd, bde) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgd), bge)) → new_ltEs7(zzz24002, zzz2200002, bgd, bge)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), daf) → False
new_esEs5(Just(zzz5000), Nothing, daf) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cee, cdc) → False
new_compare211(zzz240, zzz22000, True, bdd, bde) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cgc), cgd), cfh) → new_esEs7(zzz5000, zzz4000, cgc, cgd)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_esEs20(zzz24000, zzz2200000, cbf)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Ratio, cfg)) → new_ltEs5(zzz24000, zzz2200000, cfg)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cdc) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhg), bhh)) → new_ltEs7(zzz24000, zzz2200000, bhg, bhh)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, daf) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_esEs5(zzz24000, zzz2200000, cah)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bff), bfg)) → new_ltEs16(zzz24002, zzz2200002, bff, bfg)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dcg), dch), dda)) → new_ltEs10(zzz2400, zzz220000, dcg, dch, dda)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bhc)) → new_ltEs17(zzz24000, zzz2200000, bhc)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbg)) → new_esEs5(zzz5001, zzz4001, bbg)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bae)) → new_esEs5(zzz5000, zzz4000, bae)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), cda) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(zzz5000, zzz4000, baa, bab, bac)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), chc, cfh) → False
new_esEs4(Left(zzz5000), Right(zzz4000), chc, cfh) → False
new_lt11(zzz240, zzz22000, bdd, bde) → new_esEs8(new_compare19(zzz240, zzz22000, bdd, bde), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dba), dbb)) → new_esEs7(zzz5000, zzz4000, dba, dbb)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgf), cgg), cgh), cfh) → new_esEs6(zzz5000, zzz4000, cgf, cgg, cgh)
new_lt12(zzz24001, zzz2200001, app(ty_[], bec)) → new_lt6(zzz24001, zzz2200001, bec)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdd, bde) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdd, bde), bdd, bde)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdd), cde), cdc) → new_ltEs16(zzz24000, zzz2200000, cdd, cde)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_esEs20(zzz24000, zzz2200000, ha)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs10(zzz2400, zzz220000, bdf, bdg, bdh)
new_ltEs5(zzz2400, zzz220000, bbh) → new_fsEs(new_compare9(zzz2400, zzz220000, bbh))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs10(zzz24001, zzz2200001, ccc, ccd, cce)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cfh) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bfh)) → new_ltEs17(zzz24002, zzz2200002, bfh)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcf)) → new_esEs18(zzz5000, zzz4000, bcf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ced), cdc) → new_ltEs5(zzz24000, zzz2200000, ced)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbh), cca)) → new_ltEs16(zzz24001, zzz2200001, cbh, cca)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dbc)) → new_esEs18(zzz5000, zzz4000, dbc)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcd), dce)) → new_ltEs16(zzz2400, zzz220000, dcd, dce)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dag), dah)) → new_esEs4(zzz5000, zzz4000, dag, dah)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cdg), cdh), cea), cdc) → new_ltEs10(zzz24000, zzz2200000, cdg, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_esEs20(zzz24001, zzz2200001, bfd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_lt12(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs5(x0, x1, x2)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_@0)
new_ltEs14(True, False)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Integer)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True)
new_gt(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_@0)
new_esEs18([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs15(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt15(x0, x1)
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare32(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare25(x0, x1, True)
new_compare19(x0, x1, x2, x3)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_ltEs20(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs5(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Double)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt12(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18([], [], x0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare211(x0, x1, True, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Integer)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Int)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs12(x0, x1, x2)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1, x2)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt13(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_compare32(x0, x1, ty_Bool)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_@0)
new_compare32(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Integer)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_ltEs4(x0, x1)
new_ltEs17(Nothing, Nothing, x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_pePe(True, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs21(x0, x1, ty_@0)
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))

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

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



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

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

new_intersectFM_C2Elt106(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz642, zzz643, zzz644, zzz645, zzz646, False, h, ba, bb) → new_intersectFM_C2Elt103(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz642, zzz643, zzz644, zzz645, zzz646, new_gt(Right(zzz641), zzz642, ba, bb), h, ba, bb)
new_intersectFM_C2Elt105(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz642, zzz643, zzz644, zzz645, zzz646, h, ba, bb) → new_intersectFM_C2Elt106(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz642, zzz643, zzz644, zzz645, zzz646, new_lt11(Right(zzz641), zzz642, ba, bb), h, ba, bb)
new_intersectFM_C2Elt104(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, Branch(zzz6450, zzz6451, zzz6452, zzz6453, zzz6454), h, ba, bb) → new_intersectFM_C2Elt105(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz6450, zzz6451, zzz6452, zzz6453, zzz6454, h, ba, bb)
new_intersectFM_C2Elt106(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz642, zzz643, zzz644, Branch(zzz6450, zzz6451, zzz6452, zzz6453, zzz6454), zzz646, True, h, ba, bb) → new_intersectFM_C2Elt105(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz6450, zzz6451, zzz6452, zzz6453, zzz6454, h, ba, bb)
new_intersectFM_C2Elt103(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz642, zzz643, zzz644, zzz645, zzz646, True, h, ba, bb) → new_intersectFM_C2Elt104(zzz636, zzz637, zzz638, zzz639, zzz640, zzz641, zzz646, h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdd, bde) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bde), bdd, bde)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dcc)) → new_ltEs12(zzz2400, zzz220000, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dca, dcb) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(zzz5000, zzz4000, daa, dab, dac)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, ded), dee)) → new_compare5(zzz24000, zzz2200000, ded, dee)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdd, bde) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdd), bdd, bde)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Maybe, dae)) → new_esEs5(zzz5000, zzz4000, dae)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, cch)) → new_ltEs5(zzz24001, zzz2200001, cch)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgf)) → new_ltEs5(zzz24002, zzz2200002, bgf)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cee), cdc)) → new_ltEs16(zzz2400, zzz220000, cee, cdc)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_lt4(zzz24001, zzz2200001, bfb, bfc)
new_primCompAux0(zzz24000, zzz2200000, zzz257, cda) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, cda))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgh)) → new_ltEs12(zzz24000, zzz2200000, bgh)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cdc) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt18(zzz24000, zzz2200000, cba, cbb, cbc)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cae)) → new_lt6(zzz24000, zzz2200000, cae)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbg)) → new_esEs20(zzz5000, zzz4000, dbg)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bca) → new_asAs(new_esEs23(zzz5000, zzz4000, bca), new_esEs18(zzz5001, zzz4001, bca))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, caa)) → new_ltEs5(zzz24000, zzz2200000, caa)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cfh) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cdc) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, ha) → new_esEs8(new_compare9(zzz24000, zzz2200000, ha), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), cda) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, cda), cda)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbh)) → new_esEs5(zzz5000, zzz4000, dbh)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_ltEs10(zzz24000, zzz2200000, bhd, bhe, bhf)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfe)) → new_ltEs12(zzz24002, zzz2200002, bfe)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_[], cef)) → new_ltEs12(zzz24000, zzz2200000, cef)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, def)) → new_compare9(zzz24000, zzz2200000, def)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), cac, cad) → new_pePe(new_lt20(zzz24000, zzz2200000, cac), new_asAs(new_esEs28(zzz24000, zzz2200000, cac), new_ltEs19(zzz24001, zzz2200001, cad)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cfh) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_esEs7(zzz24001, zzz2200001, bfb, bfc)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_esEs4(zzz24001, zzz2200001, bed, bee)
new_esEs18(:(zzz5000, zzz5001), [], bca) → False
new_esEs18([], :(zzz4000, zzz4001), bca) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, baf), bag)) → new_esEs4(zzz5001, zzz4001, baf, bag)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bgg) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bgg)) → new_ltEs17(zzz2400, zzz220000, bgg)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdf), cdc) → new_ltEs17(zzz24000, zzz2200000, cdf)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], cda)) → new_ltEs12(zzz2400, zzz220000, cda)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, cac), cad)) → new_ltEs7(zzz2400, zzz220000, cac, cad)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_@2, chf), chg)) → new_esEs7(zzz5000, zzz4000, chf, chg)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_lt9(zzz24000, zzz2200000, cbf)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], cda) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_@2, cfe), cff)) → new_ltEs7(zzz24000, zzz2200000, cfe, cff)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bec)) → new_esEs18(zzz24001, zzz2200001, bec)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcf)) → new_ltEs17(zzz2400, zzz220000, dcf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, bah), bba)) → new_esEs7(zzz5001, zzz4001, bah, bba)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dca, dcb) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bha), bhb)) → new_ltEs16(zzz24000, zzz2200000, bha, bhb)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cha), cfh) → new_esEs20(zzz5000, zzz4000, cha)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bbb)) → new_esEs18(zzz5001, zzz4001, bbb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cdc) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_Either, chd), che)) → new_esEs4(zzz5000, zzz4000, chd, che)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bdb)) → new_esEs20(zzz5000, zzz4000, bdb)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(zzz5001, zzz4001, bbc, bbd, bbe)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cga), cgb), cfh) → new_esEs4(zzz5000, zzz4000, cga, cgb)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Ratio, dad)) → new_esEs20(zzz5000, zzz4000, dad)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cfh) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_lt17(zzz24001, zzz2200001, bef)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cfh) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hh)) → new_esEs18(zzz5000, zzz4000, hh)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cab) → new_asAs(new_esEs26(zzz5000, zzz4000, cab), new_esEs27(zzz5001, zzz4001, cab))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hf), hg)) → new_esEs7(zzz5000, zzz4000, hf, hg)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hd), he)) → new_esEs4(zzz5000, zzz4000, hd, he)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_Either, ceg), ceh)) → new_ltEs16(zzz24000, zzz2200000, ceg, ceh)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbh)) → new_ltEs5(zzz2400, zzz220000, bbh)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbf)) → new_esEs20(zzz5001, zzz4001, bbf)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bad)) → new_esEs20(zzz5000, zzz4000, bad)
new_compare32(zzz24000, zzz2200000, app(ty_[], dde)) → new_compare0(zzz24000, zzz2200000, dde)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_lt11(zzz24000, zzz2200000, bea, beb)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_esEs7(zzz24000, zzz2200000, cbd, cbe)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cdc) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cdc) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cfh) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_esEs5(zzz24001, zzz2200001, bef)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cfh) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddd)) → new_ltEs5(zzz2400, zzz220000, ddd)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdf, bdg, bdh) → new_pePe(new_lt13(zzz24000, zzz2200000, bdf), new_asAs(new_esEs24(zzz24000, zzz2200000, bdf), new_pePe(new_lt12(zzz24001, zzz2200001, bdg), new_asAs(new_esEs25(zzz24001, zzz2200001, bdg), new_ltEs11(zzz24002, zzz2200002, bdh)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cdc) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs10(zzz24000, zzz2200000, cfb, cfc, cfd)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_lt4(zzz24000, zzz2200000, cbd, cbe)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Maybe, cfa)) → new_ltEs17(zzz24000, zzz2200000, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_lt9(zzz24001, zzz2200001, bfd)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, cda) → new_fsEs(new_compare0(zzz2400, zzz220000, cda))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, ceb), cec), cdc) → new_ltEs7(zzz24000, zzz2200000, ceb, cec)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), hb, hc) → new_asAs(new_esEs21(zzz5000, zzz4000, hb), new_esEs22(zzz5001, zzz4001, hc))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_[], chh)) → new_esEs18(zzz5000, zzz4000, chh)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cee, cdc) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbg)) → new_ltEs12(zzz24001, zzz2200001, cbg)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cdc) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_lt17(zzz24000, zzz2200000, cah)
new_compare0(:(zzz24000, zzz24001), [], cda) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cfh) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, dea), deb), dec)) → new_compare26(zzz24000, zzz2200000, dea, deb, dec)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_lt9(zzz24000, zzz2200000, ha)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_lt18(zzz24001, zzz2200001, beg, beh, bfa)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bga), bgb), bgc)) → new_ltEs10(zzz24002, zzz2200002, bga, bgb, bgc)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bcb), bcc)) → new_esEs4(zzz5000, zzz4000, bcb, bcc)
new_ltEs17(Nothing, Just(zzz2200000), bgg) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(zzz24000, zzz2200000, cba, cbb, cbc)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_esEs4(zzz24000, zzz2200000, bea, beb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, ddb), ddc)) → new_ltEs7(zzz2400, zzz220000, ddb, ddc)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bgg) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_lt11(zzz24000, zzz2200000, caf, cag)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_lt11(zzz24001, zzz2200001, bed, bee)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, ccb)) → new_ltEs17(zzz24001, zzz2200001, ccb)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cdb), cdc) → new_ltEs12(zzz24000, zzz2200000, cdb)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs6(zzz5000, zzz4000, dbd, dbe, dbf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cae)) → new_esEs18(zzz24000, zzz2200000, cae)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccf), ccg)) → new_ltEs7(zzz24001, zzz2200001, ccf, ccg)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_gt(zzz3510, zzz4870, gg, gh) → new_esEs8(new_compare19(zzz3510, zzz4870, gg, gh), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddh)) → new_compare31(zzz24000, zzz2200000, ddh)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bca) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zzz5000, zzz4000, bcg, bch, bda)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddf), ddg)) → new_compare19(zzz24000, zzz2200000, ddf, ddg)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcd), bce)) → new_esEs7(zzz5000, zzz4000, bcd, bce)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, chb), cfh) → new_esEs5(zzz5000, zzz4000, chb)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_esEs4(zzz24000, zzz2200000, caf, cag)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdd, bde) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bdc)) → new_esEs5(zzz5000, zzz4000, bdc)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zzz24001, zzz2200001, beg, beh, bfa)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cge), cfh) → new_esEs18(zzz5000, zzz4000, cge)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdd, bde) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgd), bge)) → new_ltEs7(zzz24002, zzz2200002, bgd, bge)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), daf) → False
new_esEs5(Just(zzz5000), Nothing, daf) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cee, cdc) → False
new_compare211(zzz240, zzz22000, True, bdd, bde) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cgc), cgd), cfh) → new_esEs7(zzz5000, zzz4000, cgc, cgd)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_esEs20(zzz24000, zzz2200000, cbf)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Ratio, cfg)) → new_ltEs5(zzz24000, zzz2200000, cfg)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cdc) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhg), bhh)) → new_ltEs7(zzz24000, zzz2200000, bhg, bhh)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, daf) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_esEs5(zzz24000, zzz2200000, cah)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bff), bfg)) → new_ltEs16(zzz24002, zzz2200002, bff, bfg)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dcg), dch), dda)) → new_ltEs10(zzz2400, zzz220000, dcg, dch, dda)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bhc)) → new_ltEs17(zzz24000, zzz2200000, bhc)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbg)) → new_esEs5(zzz5001, zzz4001, bbg)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bae)) → new_esEs5(zzz5000, zzz4000, bae)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), cda) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(zzz5000, zzz4000, baa, bab, bac)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), chc, cfh) → False
new_esEs4(Left(zzz5000), Right(zzz4000), chc, cfh) → False
new_lt11(zzz240, zzz22000, bdd, bde) → new_esEs8(new_compare19(zzz240, zzz22000, bdd, bde), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dba), dbb)) → new_esEs7(zzz5000, zzz4000, dba, dbb)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgf), cgg), cgh), cfh) → new_esEs6(zzz5000, zzz4000, cgf, cgg, cgh)
new_lt12(zzz24001, zzz2200001, app(ty_[], bec)) → new_lt6(zzz24001, zzz2200001, bec)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdd, bde) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdd, bde), bdd, bde)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdd), cde), cdc) → new_ltEs16(zzz24000, zzz2200000, cdd, cde)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_esEs20(zzz24000, zzz2200000, ha)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs10(zzz2400, zzz220000, bdf, bdg, bdh)
new_ltEs5(zzz2400, zzz220000, bbh) → new_fsEs(new_compare9(zzz2400, zzz220000, bbh))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs10(zzz24001, zzz2200001, ccc, ccd, cce)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cfh) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bfh)) → new_ltEs17(zzz24002, zzz2200002, bfh)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcf)) → new_esEs18(zzz5000, zzz4000, bcf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ced), cdc) → new_ltEs5(zzz24000, zzz2200000, ced)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbh), cca)) → new_ltEs16(zzz24001, zzz2200001, cbh, cca)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dbc)) → new_esEs18(zzz5000, zzz4000, dbc)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcd), dce)) → new_ltEs16(zzz2400, zzz220000, dcd, dce)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dag), dah)) → new_esEs4(zzz5000, zzz4000, dag, dah)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cdg), cdh), cea), cdc) → new_ltEs10(zzz24000, zzz2200000, cdg, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_esEs20(zzz24001, zzz2200001, bfd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_lt12(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs5(x0, x1, x2)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_@0)
new_ltEs14(True, False)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Integer)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True)
new_gt(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_@0)
new_esEs18([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs15(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt15(x0, x1)
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare32(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare25(x0, x1, True)
new_compare19(x0, x1, x2, x3)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_ltEs20(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs5(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Double)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt12(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18([], [], x0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare211(x0, x1, True, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Integer)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Int)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs12(x0, x1, x2)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1, x2)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt13(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_compare32(x0, x1, ty_Bool)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_@0)
new_compare32(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Integer)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_ltEs4(x0, x1)
new_ltEs17(Nothing, Nothing, x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_pePe(True, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs21(x0, x1, ty_@0)
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_intersectFM_C2Elt108(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, Branch(zzz6330, zzz6331, zzz6332, zzz6333, zzz6334), h, ba, bb) → new_intersectFM_C2Elt109(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, h, ba, bb)
new_intersectFM_C2Elt109(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz630, zzz631, zzz632, zzz633, zzz634, h, ba, bb) → new_intersectFM_C2Elt1010(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz630, zzz631, zzz632, zzz633, zzz634, new_lt11(Left(zzz629), zzz630, ba, bb), h, ba, bb)
new_intersectFM_C2Elt1010(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz630, zzz631, zzz632, Branch(zzz6330, zzz6331, zzz6332, zzz6333, zzz6334), zzz634, True, h, ba, bb) → new_intersectFM_C2Elt109(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, h, ba, bb)
new_intersectFM_C2Elt107(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz630, zzz631, zzz632, zzz633, zzz634, True, h, ba, bb) → new_intersectFM_C2Elt108(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz634, h, ba, bb)
new_intersectFM_C2Elt1010(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz630, zzz631, zzz632, zzz633, zzz634, False, h, ba, bb) → new_intersectFM_C2Elt107(zzz624, zzz625, zzz626, zzz627, zzz628, zzz629, zzz630, zzz631, zzz632, zzz633, zzz634, new_gt(Left(zzz629), zzz630, ba, bb), h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdd, bde) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bde), bdd, bde)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dcc)) → new_ltEs12(zzz2400, zzz220000, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dca, dcb) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(zzz5000, zzz4000, daa, dab, dac)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, ded), dee)) → new_compare5(zzz24000, zzz2200000, ded, dee)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdd, bde) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdd), bdd, bde)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Maybe, dae)) → new_esEs5(zzz5000, zzz4000, dae)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, cch)) → new_ltEs5(zzz24001, zzz2200001, cch)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgf)) → new_ltEs5(zzz24002, zzz2200002, bgf)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cee), cdc)) → new_ltEs16(zzz2400, zzz220000, cee, cdc)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_lt4(zzz24001, zzz2200001, bfb, bfc)
new_primCompAux0(zzz24000, zzz2200000, zzz257, cda) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, cda))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgh)) → new_ltEs12(zzz24000, zzz2200000, bgh)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cdc) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt18(zzz24000, zzz2200000, cba, cbb, cbc)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cae)) → new_lt6(zzz24000, zzz2200000, cae)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbg)) → new_esEs20(zzz5000, zzz4000, dbg)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bca) → new_asAs(new_esEs23(zzz5000, zzz4000, bca), new_esEs18(zzz5001, zzz4001, bca))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, caa)) → new_ltEs5(zzz24000, zzz2200000, caa)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cfh) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cdc) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, ha) → new_esEs8(new_compare9(zzz24000, zzz2200000, ha), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), cda) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, cda), cda)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbh)) → new_esEs5(zzz5000, zzz4000, dbh)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_ltEs10(zzz24000, zzz2200000, bhd, bhe, bhf)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfe)) → new_ltEs12(zzz24002, zzz2200002, bfe)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_[], cef)) → new_ltEs12(zzz24000, zzz2200000, cef)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, def)) → new_compare9(zzz24000, zzz2200000, def)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), cac, cad) → new_pePe(new_lt20(zzz24000, zzz2200000, cac), new_asAs(new_esEs28(zzz24000, zzz2200000, cac), new_ltEs19(zzz24001, zzz2200001, cad)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cfh) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_esEs7(zzz24001, zzz2200001, bfb, bfc)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_esEs4(zzz24001, zzz2200001, bed, bee)
new_esEs18(:(zzz5000, zzz5001), [], bca) → False
new_esEs18([], :(zzz4000, zzz4001), bca) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, baf), bag)) → new_esEs4(zzz5001, zzz4001, baf, bag)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bgg) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bgg)) → new_ltEs17(zzz2400, zzz220000, bgg)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdf), cdc) → new_ltEs17(zzz24000, zzz2200000, cdf)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], cda)) → new_ltEs12(zzz2400, zzz220000, cda)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, cac), cad)) → new_ltEs7(zzz2400, zzz220000, cac, cad)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_@2, chf), chg)) → new_esEs7(zzz5000, zzz4000, chf, chg)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_lt9(zzz24000, zzz2200000, cbf)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], cda) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_@2, cfe), cff)) → new_ltEs7(zzz24000, zzz2200000, cfe, cff)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bec)) → new_esEs18(zzz24001, zzz2200001, bec)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcf)) → new_ltEs17(zzz2400, zzz220000, dcf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, bah), bba)) → new_esEs7(zzz5001, zzz4001, bah, bba)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dca, dcb) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bha), bhb)) → new_ltEs16(zzz24000, zzz2200000, bha, bhb)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cha), cfh) → new_esEs20(zzz5000, zzz4000, cha)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bbb)) → new_esEs18(zzz5001, zzz4001, bbb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cdc) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_Either, chd), che)) → new_esEs4(zzz5000, zzz4000, chd, che)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bdb)) → new_esEs20(zzz5000, zzz4000, bdb)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(zzz5001, zzz4001, bbc, bbd, bbe)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cga), cgb), cfh) → new_esEs4(zzz5000, zzz4000, cga, cgb)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Ratio, dad)) → new_esEs20(zzz5000, zzz4000, dad)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cfh) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_lt17(zzz24001, zzz2200001, bef)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cfh) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hh)) → new_esEs18(zzz5000, zzz4000, hh)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cab) → new_asAs(new_esEs26(zzz5000, zzz4000, cab), new_esEs27(zzz5001, zzz4001, cab))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hf), hg)) → new_esEs7(zzz5000, zzz4000, hf, hg)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hd), he)) → new_esEs4(zzz5000, zzz4000, hd, he)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_Either, ceg), ceh)) → new_ltEs16(zzz24000, zzz2200000, ceg, ceh)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbh)) → new_ltEs5(zzz2400, zzz220000, bbh)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbf)) → new_esEs20(zzz5001, zzz4001, bbf)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bad)) → new_esEs20(zzz5000, zzz4000, bad)
new_compare32(zzz24000, zzz2200000, app(ty_[], dde)) → new_compare0(zzz24000, zzz2200000, dde)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_lt11(zzz24000, zzz2200000, bea, beb)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_esEs7(zzz24000, zzz2200000, cbd, cbe)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cdc) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cdc) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cfh) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_esEs5(zzz24001, zzz2200001, bef)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cfh) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddd)) → new_ltEs5(zzz2400, zzz220000, ddd)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdf, bdg, bdh) → new_pePe(new_lt13(zzz24000, zzz2200000, bdf), new_asAs(new_esEs24(zzz24000, zzz2200000, bdf), new_pePe(new_lt12(zzz24001, zzz2200001, bdg), new_asAs(new_esEs25(zzz24001, zzz2200001, bdg), new_ltEs11(zzz24002, zzz2200002, bdh)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cdc) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs10(zzz24000, zzz2200000, cfb, cfc, cfd)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_lt4(zzz24000, zzz2200000, cbd, cbe)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Maybe, cfa)) → new_ltEs17(zzz24000, zzz2200000, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_lt9(zzz24001, zzz2200001, bfd)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, cda) → new_fsEs(new_compare0(zzz2400, zzz220000, cda))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, ceb), cec), cdc) → new_ltEs7(zzz24000, zzz2200000, ceb, cec)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), hb, hc) → new_asAs(new_esEs21(zzz5000, zzz4000, hb), new_esEs22(zzz5001, zzz4001, hc))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_[], chh)) → new_esEs18(zzz5000, zzz4000, chh)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cee, cdc) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbg)) → new_ltEs12(zzz24001, zzz2200001, cbg)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cdc) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_lt17(zzz24000, zzz2200000, cah)
new_compare0(:(zzz24000, zzz24001), [], cda) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cfh) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, dea), deb), dec)) → new_compare26(zzz24000, zzz2200000, dea, deb, dec)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_lt9(zzz24000, zzz2200000, ha)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_lt18(zzz24001, zzz2200001, beg, beh, bfa)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bga), bgb), bgc)) → new_ltEs10(zzz24002, zzz2200002, bga, bgb, bgc)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bcb), bcc)) → new_esEs4(zzz5000, zzz4000, bcb, bcc)
new_ltEs17(Nothing, Just(zzz2200000), bgg) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(zzz24000, zzz2200000, cba, cbb, cbc)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_esEs4(zzz24000, zzz2200000, bea, beb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, ddb), ddc)) → new_ltEs7(zzz2400, zzz220000, ddb, ddc)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bgg) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_lt11(zzz24000, zzz2200000, caf, cag)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_lt11(zzz24001, zzz2200001, bed, bee)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, ccb)) → new_ltEs17(zzz24001, zzz2200001, ccb)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cdb), cdc) → new_ltEs12(zzz24000, zzz2200000, cdb)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs6(zzz5000, zzz4000, dbd, dbe, dbf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cae)) → new_esEs18(zzz24000, zzz2200000, cae)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccf), ccg)) → new_ltEs7(zzz24001, zzz2200001, ccf, ccg)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_gt(zzz3510, zzz4870, gg, gh) → new_esEs8(new_compare19(zzz3510, zzz4870, gg, gh), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddh)) → new_compare31(zzz24000, zzz2200000, ddh)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bca) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zzz5000, zzz4000, bcg, bch, bda)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddf), ddg)) → new_compare19(zzz24000, zzz2200000, ddf, ddg)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcd), bce)) → new_esEs7(zzz5000, zzz4000, bcd, bce)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, chb), cfh) → new_esEs5(zzz5000, zzz4000, chb)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_esEs4(zzz24000, zzz2200000, caf, cag)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdd, bde) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bdc)) → new_esEs5(zzz5000, zzz4000, bdc)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zzz24001, zzz2200001, beg, beh, bfa)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cge), cfh) → new_esEs18(zzz5000, zzz4000, cge)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdd, bde) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgd), bge)) → new_ltEs7(zzz24002, zzz2200002, bgd, bge)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), daf) → False
new_esEs5(Just(zzz5000), Nothing, daf) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cee, cdc) → False
new_compare211(zzz240, zzz22000, True, bdd, bde) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cgc), cgd), cfh) → new_esEs7(zzz5000, zzz4000, cgc, cgd)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_esEs20(zzz24000, zzz2200000, cbf)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Ratio, cfg)) → new_ltEs5(zzz24000, zzz2200000, cfg)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cdc) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhg), bhh)) → new_ltEs7(zzz24000, zzz2200000, bhg, bhh)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, daf) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_esEs5(zzz24000, zzz2200000, cah)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bff), bfg)) → new_ltEs16(zzz24002, zzz2200002, bff, bfg)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dcg), dch), dda)) → new_ltEs10(zzz2400, zzz220000, dcg, dch, dda)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bhc)) → new_ltEs17(zzz24000, zzz2200000, bhc)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbg)) → new_esEs5(zzz5001, zzz4001, bbg)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bae)) → new_esEs5(zzz5000, zzz4000, bae)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), cda) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(zzz5000, zzz4000, baa, bab, bac)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), chc, cfh) → False
new_esEs4(Left(zzz5000), Right(zzz4000), chc, cfh) → False
new_lt11(zzz240, zzz22000, bdd, bde) → new_esEs8(new_compare19(zzz240, zzz22000, bdd, bde), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dba), dbb)) → new_esEs7(zzz5000, zzz4000, dba, dbb)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgf), cgg), cgh), cfh) → new_esEs6(zzz5000, zzz4000, cgf, cgg, cgh)
new_lt12(zzz24001, zzz2200001, app(ty_[], bec)) → new_lt6(zzz24001, zzz2200001, bec)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdd, bde) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdd, bde), bdd, bde)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdd), cde), cdc) → new_ltEs16(zzz24000, zzz2200000, cdd, cde)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_esEs20(zzz24000, zzz2200000, ha)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs10(zzz2400, zzz220000, bdf, bdg, bdh)
new_ltEs5(zzz2400, zzz220000, bbh) → new_fsEs(new_compare9(zzz2400, zzz220000, bbh))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs10(zzz24001, zzz2200001, ccc, ccd, cce)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cfh) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bfh)) → new_ltEs17(zzz24002, zzz2200002, bfh)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcf)) → new_esEs18(zzz5000, zzz4000, bcf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ced), cdc) → new_ltEs5(zzz24000, zzz2200000, ced)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbh), cca)) → new_ltEs16(zzz24001, zzz2200001, cbh, cca)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dbc)) → new_esEs18(zzz5000, zzz4000, dbc)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcd), dce)) → new_ltEs16(zzz2400, zzz220000, dcd, dce)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dag), dah)) → new_esEs4(zzz5000, zzz4000, dag, dah)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cdg), cdh), cea), cdc) → new_ltEs10(zzz24000, zzz2200000, cdg, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_esEs20(zzz24001, zzz2200001, bfd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_lt12(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs5(x0, x1, x2)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_@0)
new_ltEs14(True, False)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Integer)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True)
new_gt(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_@0)
new_esEs18([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs15(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt15(x0, x1)
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare32(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare25(x0, x1, True)
new_compare19(x0, x1, x2, x3)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_ltEs20(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs5(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Double)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt12(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18([], [], x0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare211(x0, x1, True, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Integer)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Int)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs12(x0, x1, x2)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1, x2)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt13(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_compare32(x0, x1, ty_Bool)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_@0)
new_compare32(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Integer)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_ltEs4(x0, x1)
new_ltEs17(Nothing, Nothing, x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_pePe(True, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs21(x0, x1, ty_@0)
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_intersectFM_C2Elt1014(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz608, zzz609, zzz610, zzz611, zzz612, False, h, ba, bb) → new_intersectFM_C2Elt1011(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz608, zzz609, zzz610, zzz611, zzz612, new_gt(Left(zzz607), zzz608, ba, bb), h, ba, bb)
new_intersectFM_C2Elt1014(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz608, zzz609, zzz610, Branch(zzz6110, zzz6111, zzz6112, zzz6113, zzz6114), zzz612, True, h, ba, bb) → new_intersectFM_C2Elt1013(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz6110, zzz6111, zzz6112, zzz6113, zzz6114, h, ba, bb)
new_intersectFM_C2Elt1011(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz608, zzz609, zzz610, zzz611, zzz612, True, h, ba, bb) → new_intersectFM_C2Elt1012(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz612, h, ba, bb)
new_intersectFM_C2Elt1012(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, Branch(zzz6110, zzz6111, zzz6112, zzz6113, zzz6114), h, ba, bb) → new_intersectFM_C2Elt1013(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz6110, zzz6111, zzz6112, zzz6113, zzz6114, h, ba, bb)
new_intersectFM_C2Elt1013(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz608, zzz609, zzz610, zzz611, zzz612, h, ba, bb) → new_intersectFM_C2Elt1014(zzz602, zzz603, zzz604, zzz605, zzz606, zzz607, zzz608, zzz609, zzz610, zzz611, zzz612, new_lt11(Left(zzz607), zzz608, ba, bb), h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdd, bde) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bde), bdd, bde)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dcc)) → new_ltEs12(zzz2400, zzz220000, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dca, dcb) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(zzz5000, zzz4000, daa, dab, dac)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, ded), dee)) → new_compare5(zzz24000, zzz2200000, ded, dee)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdd, bde) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdd), bdd, bde)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Maybe, dae)) → new_esEs5(zzz5000, zzz4000, dae)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, cch)) → new_ltEs5(zzz24001, zzz2200001, cch)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgf)) → new_ltEs5(zzz24002, zzz2200002, bgf)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cee), cdc)) → new_ltEs16(zzz2400, zzz220000, cee, cdc)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_lt4(zzz24001, zzz2200001, bfb, bfc)
new_primCompAux0(zzz24000, zzz2200000, zzz257, cda) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, cda))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgh)) → new_ltEs12(zzz24000, zzz2200000, bgh)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cdc) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt18(zzz24000, zzz2200000, cba, cbb, cbc)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cae)) → new_lt6(zzz24000, zzz2200000, cae)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbg)) → new_esEs20(zzz5000, zzz4000, dbg)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bca) → new_asAs(new_esEs23(zzz5000, zzz4000, bca), new_esEs18(zzz5001, zzz4001, bca))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, caa)) → new_ltEs5(zzz24000, zzz2200000, caa)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cfh) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cdc) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, ha) → new_esEs8(new_compare9(zzz24000, zzz2200000, ha), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), cda) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, cda), cda)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbh)) → new_esEs5(zzz5000, zzz4000, dbh)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_ltEs10(zzz24000, zzz2200000, bhd, bhe, bhf)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfe)) → new_ltEs12(zzz24002, zzz2200002, bfe)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_[], cef)) → new_ltEs12(zzz24000, zzz2200000, cef)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, def)) → new_compare9(zzz24000, zzz2200000, def)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), cac, cad) → new_pePe(new_lt20(zzz24000, zzz2200000, cac), new_asAs(new_esEs28(zzz24000, zzz2200000, cac), new_ltEs19(zzz24001, zzz2200001, cad)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cfh) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_esEs7(zzz24001, zzz2200001, bfb, bfc)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_esEs4(zzz24001, zzz2200001, bed, bee)
new_esEs18(:(zzz5000, zzz5001), [], bca) → False
new_esEs18([], :(zzz4000, zzz4001), bca) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, baf), bag)) → new_esEs4(zzz5001, zzz4001, baf, bag)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bgg) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bgg)) → new_ltEs17(zzz2400, zzz220000, bgg)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdf), cdc) → new_ltEs17(zzz24000, zzz2200000, cdf)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], cda)) → new_ltEs12(zzz2400, zzz220000, cda)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, cac), cad)) → new_ltEs7(zzz2400, zzz220000, cac, cad)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_@2, chf), chg)) → new_esEs7(zzz5000, zzz4000, chf, chg)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_lt9(zzz24000, zzz2200000, cbf)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], cda) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_@2, cfe), cff)) → new_ltEs7(zzz24000, zzz2200000, cfe, cff)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bec)) → new_esEs18(zzz24001, zzz2200001, bec)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcf)) → new_ltEs17(zzz2400, zzz220000, dcf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, bah), bba)) → new_esEs7(zzz5001, zzz4001, bah, bba)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dca, dcb) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bha), bhb)) → new_ltEs16(zzz24000, zzz2200000, bha, bhb)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cha), cfh) → new_esEs20(zzz5000, zzz4000, cha)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bbb)) → new_esEs18(zzz5001, zzz4001, bbb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cdc) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_Either, chd), che)) → new_esEs4(zzz5000, zzz4000, chd, che)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bdb)) → new_esEs20(zzz5000, zzz4000, bdb)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(zzz5001, zzz4001, bbc, bbd, bbe)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cga), cgb), cfh) → new_esEs4(zzz5000, zzz4000, cga, cgb)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Ratio, dad)) → new_esEs20(zzz5000, zzz4000, dad)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cfh) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_lt17(zzz24001, zzz2200001, bef)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cfh) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hh)) → new_esEs18(zzz5000, zzz4000, hh)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cab) → new_asAs(new_esEs26(zzz5000, zzz4000, cab), new_esEs27(zzz5001, zzz4001, cab))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hf), hg)) → new_esEs7(zzz5000, zzz4000, hf, hg)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hd), he)) → new_esEs4(zzz5000, zzz4000, hd, he)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_Either, ceg), ceh)) → new_ltEs16(zzz24000, zzz2200000, ceg, ceh)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbh)) → new_ltEs5(zzz2400, zzz220000, bbh)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbf)) → new_esEs20(zzz5001, zzz4001, bbf)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bad)) → new_esEs20(zzz5000, zzz4000, bad)
new_compare32(zzz24000, zzz2200000, app(ty_[], dde)) → new_compare0(zzz24000, zzz2200000, dde)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_lt11(zzz24000, zzz2200000, bea, beb)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_esEs7(zzz24000, zzz2200000, cbd, cbe)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cdc) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cdc) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cfh) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_esEs5(zzz24001, zzz2200001, bef)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cfh) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddd)) → new_ltEs5(zzz2400, zzz220000, ddd)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdf, bdg, bdh) → new_pePe(new_lt13(zzz24000, zzz2200000, bdf), new_asAs(new_esEs24(zzz24000, zzz2200000, bdf), new_pePe(new_lt12(zzz24001, zzz2200001, bdg), new_asAs(new_esEs25(zzz24001, zzz2200001, bdg), new_ltEs11(zzz24002, zzz2200002, bdh)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cdc) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs10(zzz24000, zzz2200000, cfb, cfc, cfd)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_lt4(zzz24000, zzz2200000, cbd, cbe)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Maybe, cfa)) → new_ltEs17(zzz24000, zzz2200000, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_lt9(zzz24001, zzz2200001, bfd)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, cda) → new_fsEs(new_compare0(zzz2400, zzz220000, cda))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, ceb), cec), cdc) → new_ltEs7(zzz24000, zzz2200000, ceb, cec)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), hb, hc) → new_asAs(new_esEs21(zzz5000, zzz4000, hb), new_esEs22(zzz5001, zzz4001, hc))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_[], chh)) → new_esEs18(zzz5000, zzz4000, chh)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cee, cdc) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbg)) → new_ltEs12(zzz24001, zzz2200001, cbg)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cdc) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_lt17(zzz24000, zzz2200000, cah)
new_compare0(:(zzz24000, zzz24001), [], cda) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cfh) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, dea), deb), dec)) → new_compare26(zzz24000, zzz2200000, dea, deb, dec)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_lt9(zzz24000, zzz2200000, ha)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_lt18(zzz24001, zzz2200001, beg, beh, bfa)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bga), bgb), bgc)) → new_ltEs10(zzz24002, zzz2200002, bga, bgb, bgc)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bcb), bcc)) → new_esEs4(zzz5000, zzz4000, bcb, bcc)
new_ltEs17(Nothing, Just(zzz2200000), bgg) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(zzz24000, zzz2200000, cba, cbb, cbc)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_esEs4(zzz24000, zzz2200000, bea, beb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, ddb), ddc)) → new_ltEs7(zzz2400, zzz220000, ddb, ddc)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bgg) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_lt11(zzz24000, zzz2200000, caf, cag)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_lt11(zzz24001, zzz2200001, bed, bee)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, ccb)) → new_ltEs17(zzz24001, zzz2200001, ccb)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cdb), cdc) → new_ltEs12(zzz24000, zzz2200000, cdb)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs6(zzz5000, zzz4000, dbd, dbe, dbf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cae)) → new_esEs18(zzz24000, zzz2200000, cae)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccf), ccg)) → new_ltEs7(zzz24001, zzz2200001, ccf, ccg)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_gt(zzz3510, zzz4870, gg, gh) → new_esEs8(new_compare19(zzz3510, zzz4870, gg, gh), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddh)) → new_compare31(zzz24000, zzz2200000, ddh)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bca) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zzz5000, zzz4000, bcg, bch, bda)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddf), ddg)) → new_compare19(zzz24000, zzz2200000, ddf, ddg)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcd), bce)) → new_esEs7(zzz5000, zzz4000, bcd, bce)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, chb), cfh) → new_esEs5(zzz5000, zzz4000, chb)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_esEs4(zzz24000, zzz2200000, caf, cag)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdd, bde) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bdc)) → new_esEs5(zzz5000, zzz4000, bdc)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zzz24001, zzz2200001, beg, beh, bfa)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cge), cfh) → new_esEs18(zzz5000, zzz4000, cge)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdd, bde) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgd), bge)) → new_ltEs7(zzz24002, zzz2200002, bgd, bge)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), daf) → False
new_esEs5(Just(zzz5000), Nothing, daf) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cee, cdc) → False
new_compare211(zzz240, zzz22000, True, bdd, bde) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cgc), cgd), cfh) → new_esEs7(zzz5000, zzz4000, cgc, cgd)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_esEs20(zzz24000, zzz2200000, cbf)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Ratio, cfg)) → new_ltEs5(zzz24000, zzz2200000, cfg)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cdc) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhg), bhh)) → new_ltEs7(zzz24000, zzz2200000, bhg, bhh)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, daf) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_esEs5(zzz24000, zzz2200000, cah)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bff), bfg)) → new_ltEs16(zzz24002, zzz2200002, bff, bfg)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dcg), dch), dda)) → new_ltEs10(zzz2400, zzz220000, dcg, dch, dda)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bhc)) → new_ltEs17(zzz24000, zzz2200000, bhc)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbg)) → new_esEs5(zzz5001, zzz4001, bbg)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bae)) → new_esEs5(zzz5000, zzz4000, bae)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), cda) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(zzz5000, zzz4000, baa, bab, bac)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), chc, cfh) → False
new_esEs4(Left(zzz5000), Right(zzz4000), chc, cfh) → False
new_lt11(zzz240, zzz22000, bdd, bde) → new_esEs8(new_compare19(zzz240, zzz22000, bdd, bde), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dba), dbb)) → new_esEs7(zzz5000, zzz4000, dba, dbb)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgf), cgg), cgh), cfh) → new_esEs6(zzz5000, zzz4000, cgf, cgg, cgh)
new_lt12(zzz24001, zzz2200001, app(ty_[], bec)) → new_lt6(zzz24001, zzz2200001, bec)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdd, bde) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdd, bde), bdd, bde)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdd), cde), cdc) → new_ltEs16(zzz24000, zzz2200000, cdd, cde)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_esEs20(zzz24000, zzz2200000, ha)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs10(zzz2400, zzz220000, bdf, bdg, bdh)
new_ltEs5(zzz2400, zzz220000, bbh) → new_fsEs(new_compare9(zzz2400, zzz220000, bbh))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs10(zzz24001, zzz2200001, ccc, ccd, cce)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cfh) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bfh)) → new_ltEs17(zzz24002, zzz2200002, bfh)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcf)) → new_esEs18(zzz5000, zzz4000, bcf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ced), cdc) → new_ltEs5(zzz24000, zzz2200000, ced)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbh), cca)) → new_ltEs16(zzz24001, zzz2200001, cbh, cca)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dbc)) → new_esEs18(zzz5000, zzz4000, dbc)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcd), dce)) → new_ltEs16(zzz2400, zzz220000, dcd, dce)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dag), dah)) → new_esEs4(zzz5000, zzz4000, dag, dah)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cdg), cdh), cea), cdc) → new_ltEs10(zzz24000, zzz2200000, cdg, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_esEs20(zzz24001, zzz2200001, bfd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_lt12(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs5(x0, x1, x2)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_@0)
new_ltEs14(True, False)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Integer)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True)
new_gt(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_@0)
new_esEs18([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs15(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt15(x0, x1)
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare32(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare25(x0, x1, True)
new_compare19(x0, x1, x2, x3)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_ltEs20(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs5(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Double)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt12(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18([], [], x0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare211(x0, x1, True, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Integer)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Int)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs12(x0, x1, x2)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1, x2)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt13(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_compare32(x0, x1, ty_Bool)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_@0)
new_compare32(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Integer)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_ltEs4(x0, x1)
new_ltEs17(Nothing, Nothing, x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_pePe(True, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs21(x0, x1, ty_@0)
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_deleteMin(zzz3950, zzz3951, zzz3952, Branch(zzz39530, zzz39531, zzz39532, zzz39533, zzz39534), zzz3954, h, ba, bb) → new_deleteMin(zzz39530, zzz39531, zzz39532, zzz39533, zzz39534, h, ba, bb)

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

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



↳ 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
                                  ↳ QDP
                                  ↳ 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_deleteMax(zzz3960, zzz3961, zzz3962, zzz3963, Branch(zzz39640, zzz39641, zzz39642, zzz39643, zzz39644), h, ba, bb) → new_deleteMax(zzz39640, zzz39641, zzz39642, zzz39643, zzz39644, h, ba, bb)

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

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



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs8(EQ, EQ) → True
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_primMulNat0(Zero, Zero) → Zero
new_esEs8(GT, GT) → True
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs8(LT, LT) → True
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpNat0(Succ(zzz240000), Zero) → GT

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb) at position [10] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



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

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

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_lt19(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), h, ba, bb) at position [10] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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_lt19(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



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

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

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



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

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

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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_compare18(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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0,0] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_l(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb) → new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), new_sizeFM(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, h, ba, bb)), LT), h, ba, bb) at position [10,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), zzz3962), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), zzz3962), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), new_sizeFM(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, h, ba, bb)), LT), h, ba, bb) at position [10,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), zzz3962), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), zzz3962), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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(x0, x1, x2, x3, x4, x5, x6, x7)



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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), zzz3962), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, False, h, ba, bb) → new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3952), zzz3962), LT), h, ba, bb)
The remaining pairs can at least be oriented weakly.

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x3 + x4 + 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_esEs8(x1, x2)) = 0   
POL(new_glueVBal(x1, x2, x3, x4, x5)) = x1   
POL(new_glueVBal3GlueVBal1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_glueVBal3GlueVBal2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x3 + x4 + x5   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpNat0(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   

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal3GlueVBal1(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(zzz3964, Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, True, h, ba, bb) → new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), zzz3953, h, ba, bb)
new_glueVBal(Branch(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964), Branch(zzz3950, zzz3951, zzz3952, zzz3953, zzz3954), h, ba, bb) → new_glueVBal3GlueVBal2(zzz3960, zzz3961, zzz3962, zzz3963, zzz3964, zzz3950, zzz3951, zzz3952, zzz3953, zzz3954, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3962), zzz3952), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ QDP
                                  ↳ 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_addToFM_C1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, True, h, ba, bb) → new_addToFM_C(zzz4874, zzz3510, zzz3511, h, ba, bb)
new_addToFM_C(Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), zzz3510, zzz3511, h, ba, bb) → new_addToFM_C2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, new_lt11(zzz3510, zzz4870, h, ba), h, ba, bb)
new_addToFM_C2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, True, h, ba, bb) → new_addToFM_C(zzz4873, zzz3510, zzz3511, h, ba, bb)
new_addToFM_C2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, False, h, ba, bb) → new_addToFM_C1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, new_gt(zzz3510, zzz4870, h, ba), h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdb, bdc) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bdc), bdb, bdc)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dca)) → new_ltEs12(zzz2400, zzz220000, dca)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dbg, dbh) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(zzz5000, zzz4000, chg, chh, daa)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, deb), dec)) → new_compare5(zzz24000, zzz2200000, deb, dec)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdb, bdc) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdb), bdb, bdc)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Maybe, dac)) → new_esEs5(zzz5000, zzz4000, dac)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, ccf)) → new_ltEs5(zzz24001, zzz2200001, ccf)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgd)) → new_ltEs5(zzz24002, zzz2200002, bgd)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cec), cda)) → new_ltEs16(zzz2400, zzz220000, cec, cda)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_lt4(zzz24001, zzz2200001, beh, bfa)
new_primCompAux0(zzz24000, zzz2200000, zzz257, ccg) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, ccg))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgf)) → new_ltEs12(zzz24000, zzz2200000, bgf)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cda) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_lt18(zzz24000, zzz2200000, cag, cah, cba)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cac)) → new_lt6(zzz24000, zzz2200000, cac)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbe)) → new_esEs20(zzz5000, zzz4000, dbe)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bbg) → new_asAs(new_esEs23(zzz5000, zzz4000, bbg), new_esEs18(zzz5001, zzz4001, bbg))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, bhg)) → new_ltEs5(zzz24000, zzz2200000, bhg)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cff) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cda) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, gg) → new_esEs8(new_compare9(zzz24000, zzz2200000, gg), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), ccg) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, ccg), ccg)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbf)) → new_esEs5(zzz5000, zzz4000, dbf)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhb), bhc), bhd)) → new_ltEs10(zzz24000, zzz2200000, bhb, bhc, bhd)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfc)) → new_ltEs12(zzz24002, zzz2200002, bfc)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_[], ced)) → new_ltEs12(zzz24000, zzz2200000, ced)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, ded)) → new_compare9(zzz24000, zzz2200000, ded)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), caa, cab) → new_pePe(new_lt20(zzz24000, zzz2200000, caa), new_asAs(new_esEs28(zzz24000, zzz2200000, caa), new_ltEs19(zzz24001, zzz2200001, cab)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cff) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_esEs7(zzz24001, zzz2200001, beh, bfa)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_esEs4(zzz24001, zzz2200001, beb, bec)
new_esEs18(:(zzz5000, zzz5001), [], bbg) → False
new_esEs18([], :(zzz4000, zzz4001), bbg) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, bad), bae)) → new_esEs4(zzz5001, zzz4001, bad, bae)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bge) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bge)) → new_ltEs17(zzz2400, zzz220000, bge)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdd), cda) → new_ltEs17(zzz24000, zzz2200000, cdd)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], ccg)) → new_ltEs12(zzz2400, zzz220000, ccg)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, caa), cab)) → new_ltEs7(zzz2400, zzz220000, caa, cab)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_@2, chd), che)) → new_esEs7(zzz5000, zzz4000, chd, che)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_lt9(zzz24000, zzz2200000, cbd)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], ccg) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_@2, cfc), cfd)) → new_ltEs7(zzz24000, zzz2200000, cfc, cfd)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bea)) → new_esEs18(zzz24001, zzz2200001, bea)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcd)) → new_ltEs17(zzz2400, zzz220000, dcd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, baf), bag)) → new_esEs7(zzz5001, zzz4001, baf, bag)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dbg, dbh) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bgg), bgh)) → new_ltEs16(zzz24000, zzz2200000, bgg, bgh)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cgg), cff) → new_esEs20(zzz5000, zzz4000, cgg)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bah)) → new_esEs18(zzz5001, zzz4001, bah)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cda) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_Either, chb), chc)) → new_esEs4(zzz5000, zzz4000, chb, chc)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bch)) → new_esEs20(zzz5000, zzz4000, bch)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs6(zzz5001, zzz4001, bba, bbb, bbc)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cfg), cfh), cff) → new_esEs4(zzz5000, zzz4000, cfg, cfh)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Ratio, dab)) → new_esEs20(zzz5000, zzz4000, dab)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cff) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_lt17(zzz24001, zzz2200001, bed)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cff) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hf)) → new_esEs18(zzz5000, zzz4000, hf)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bhh) → new_asAs(new_esEs26(zzz5000, zzz4000, bhh), new_esEs27(zzz5001, zzz4001, bhh))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hd), he)) → new_esEs7(zzz5000, zzz4000, hd, he)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hb), hc)) → new_esEs4(zzz5000, zzz4000, hb, hc)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_Either, cee), cef)) → new_ltEs16(zzz24000, zzz2200000, cee, cef)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbf)) → new_ltEs5(zzz2400, zzz220000, bbf)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbd)) → new_esEs20(zzz5001, zzz4001, bbd)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bab)) → new_esEs20(zzz5000, zzz4000, bab)
new_compare32(zzz24000, zzz2200000, app(ty_[], ddc)) → new_compare0(zzz24000, zzz2200000, ddc)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_lt11(zzz24000, zzz2200000, bdg, bdh)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_esEs7(zzz24000, zzz2200000, cbb, cbc)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cda) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cda) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cff) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_esEs5(zzz24001, zzz2200001, bed)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cff) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddb)) → new_ltEs5(zzz2400, zzz220000, ddb)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdd, bde, bdf) → new_pePe(new_lt13(zzz24000, zzz2200000, bdd), new_asAs(new_esEs24(zzz24000, zzz2200000, bdd), new_pePe(new_lt12(zzz24001, zzz2200001, bde), new_asAs(new_esEs25(zzz24001, zzz2200001, bde), new_ltEs11(zzz24002, zzz2200002, bdf)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cda) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(app(ty_@3, ceh), cfa), cfb)) → new_ltEs10(zzz24000, zzz2200000, ceh, cfa, cfb)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_lt4(zzz24000, zzz2200000, cbb, cbc)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Maybe, ceg)) → new_ltEs17(zzz24000, zzz2200000, ceg)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_lt9(zzz24001, zzz2200001, bfb)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, ccg) → new_fsEs(new_compare0(zzz2400, zzz220000, ccg))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, cdh), cea), cda) → new_ltEs7(zzz24000, zzz2200000, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), gh, ha) → new_asAs(new_esEs21(zzz5000, zzz4000, gh), new_esEs22(zzz5001, zzz4001, ha))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_[], chf)) → new_esEs18(zzz5000, zzz4000, chf)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cec, cda) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbe)) → new_ltEs12(zzz24001, zzz2200001, cbe)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cda) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_lt17(zzz24000, zzz2200000, caf)
new_compare0(:(zzz24000, zzz24001), [], ccg) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cff) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare26(zzz24000, zzz2200000, ddg, ddh, dea)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_lt9(zzz24000, zzz2200000, gg)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_lt18(zzz24001, zzz2200001, bee, bef, beg)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bfg), bfh), bga)) → new_ltEs10(zzz24002, zzz2200002, bfg, bfh, bga)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bbh), bca)) → new_esEs4(zzz5000, zzz4000, bbh, bca)
new_ltEs17(Nothing, Just(zzz2200000), bge) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_esEs6(zzz24000, zzz2200000, cag, cah, cba)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_esEs4(zzz24000, zzz2200000, bdg, bdh)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, dch), dda)) → new_ltEs7(zzz2400, zzz220000, dch, dda)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bge) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_lt11(zzz24000, zzz2200000, cad, cae)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_lt11(zzz24001, zzz2200001, beb, bec)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, cbh)) → new_ltEs17(zzz24001, zzz2200001, cbh)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cch), cda) → new_ltEs12(zzz24000, zzz2200000, cch)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs6(zzz5000, zzz4000, dbb, dbc, dbd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cac)) → new_esEs18(zzz24000, zzz2200000, cac)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccd), cce)) → new_ltEs7(zzz24001, zzz2200001, ccd, cce)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_gt(zzz3510, zzz4870, h, ba) → new_esEs8(new_compare19(zzz3510, zzz4870, h, ba), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddf)) → new_compare31(zzz24000, zzz2200000, ddf)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bbg) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs6(zzz5000, zzz4000, bce, bcf, bcg)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddd), dde)) → new_compare19(zzz24000, zzz2200000, ddd, dde)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcb), bcc)) → new_esEs7(zzz5000, zzz4000, bcb, bcc)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, cgh), cff) → new_esEs5(zzz5000, zzz4000, cgh)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_esEs4(zzz24000, zzz2200000, cad, cae)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdb, bdc) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bda)) → new_esEs5(zzz5000, zzz4000, bda)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_esEs6(zzz24001, zzz2200001, bee, bef, beg)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cgc), cff) → new_esEs18(zzz5000, zzz4000, cgc)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdb, bdc) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgb), bgc)) → new_ltEs7(zzz24002, zzz2200002, bgb, bgc)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), dad) → False
new_esEs5(Just(zzz5000), Nothing, dad) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cec, cda) → False
new_compare211(zzz240, zzz22000, True, bdb, bdc) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cga), cgb), cff) → new_esEs7(zzz5000, zzz4000, cga, cgb)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_esEs20(zzz24000, zzz2200000, cbd)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Ratio, cfe)) → new_ltEs5(zzz24000, zzz2200000, cfe)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cda) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhe), bhf)) → new_ltEs7(zzz24000, zzz2200000, bhe, bhf)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, dad) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_esEs5(zzz24000, zzz2200000, caf)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bfd), bfe)) → new_ltEs16(zzz24002, zzz2200002, bfd, bfe)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs10(zzz2400, zzz220000, dce, dcf, dcg)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bha)) → new_ltEs17(zzz24000, zzz2200000, bha)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbe)) → new_esEs5(zzz5001, zzz4001, bbe)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bac)) → new_esEs5(zzz5000, zzz4000, bac)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), ccg) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, hg), hh), baa)) → new_esEs6(zzz5000, zzz4000, hg, hh, baa)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), cha, cff) → False
new_esEs4(Left(zzz5000), Right(zzz4000), cha, cff) → False
new_lt11(zzz240, zzz22000, bdb, bdc) → new_esEs8(new_compare19(zzz240, zzz22000, bdb, bdc), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dag), dah)) → new_esEs7(zzz5000, zzz4000, dag, dah)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgd), cge), cgf), cff) → new_esEs6(zzz5000, zzz4000, cgd, cge, cgf)
new_lt12(zzz24001, zzz2200001, app(ty_[], bea)) → new_lt6(zzz24001, zzz2200001, bea)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdb, bdc) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdb, bdc), bdb, bdc)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdb), cdc), cda) → new_ltEs16(zzz24000, zzz2200000, cdb, cdc)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_esEs20(zzz24000, zzz2200000, gg)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs10(zzz2400, zzz220000, bdd, bde, bdf)
new_ltEs5(zzz2400, zzz220000, bbf) → new_fsEs(new_compare9(zzz2400, zzz220000, bbf))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, cca), ccb), ccc)) → new_ltEs10(zzz24001, zzz2200001, cca, ccb, ccc)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cff) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bff)) → new_ltEs17(zzz24002, zzz2200002, bff)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcd)) → new_esEs18(zzz5000, zzz4000, bcd)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ceb), cda) → new_ltEs5(zzz24000, zzz2200000, ceb)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbf), cbg)) → new_ltEs16(zzz24001, zzz2200001, cbf, cbg)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dba)) → new_esEs18(zzz5000, zzz4000, dba)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcb), dcc)) → new_ltEs16(zzz2400, zzz220000, dcb, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dae), daf)) → new_esEs4(zzz5000, zzz4000, dae, daf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cde), cdf), cdg), cda) → new_ltEs10(zzz24000, zzz2200000, cde, cdf, cdg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_esEs20(zzz24001, zzz2200001, bfb)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_sr(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_compare30(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs15(x0, x1)
new_esEs10(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(True, False)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs9(x0, x1, ty_Float)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_compare211(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs18([], :(x0, x1), x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Nothing, Nothing, x0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Float)
new_ltEs12(x0, x1, x2)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs28(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_compare28(x0, x1, True)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_compare0(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18([], [], x0)
new_compare32(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs15(Char(x0), Char(x1))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt15(x0, x1)
new_fsEs(x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs17(Nothing, Just(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_gt(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare25(x0, x1, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs9(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare0([], [], x0)
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_lt7(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Integer)
new_lt12(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Float)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_ltEs17(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs11(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1)
new_ltEs13(x0, x1)
new_esEs11(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Integer)
new_lt9(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, x2, x3)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(False, False)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt13(x0, x1, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(False, False)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1)
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Float)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Bool)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, True, x2, x3)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Just(x0), x1)
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Char)
new_compare110(x0, x1, False, x2, x3)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt12(x0, x1, ty_Bool)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs21(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs8(EQ, EQ) → True
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_primMulNat0(Zero, Zero) → Zero
new_esEs8(GT, GT) → True
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs8(LT, LT) → True
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb) at position [12] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), h, ba, bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_lt19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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_lt19(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_compare18(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_compare18(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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_compare18(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_sIZE_RATIO
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)



↳ 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
                                  ↳ 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
                                                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, h, ba, bb) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, bc, bd, be) → zzz3932

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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(x0, x1, x2, x3, x4, x5, x6, x7)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x2 + x3 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 1   
POL(Neg(x1)) = 1   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(True) = 1   
POL(Zero) = 0   
POL(new_esEs8(x1, x2)) = x1   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6, x7)) = x3   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)) = x10 + x13   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)) = x10 + x7 + x8   
POL(new_primCmpInt(x1, x2)) = x2   
POL(new_primCmpNat0(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)) = 0   

The following usable rules [17] were oriented:

new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_esEs8(EQ, LT) → False
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_esEs8(GT, LT) → False
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4872), zzz35132), LT), h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, h, ba, bb) → new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, h, ba, bb)
new_mkVBalBranch(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz35132), zzz4872), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, x0)
new_esEs8(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primCmpNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(GT, GT)
new_primPlusNat0(Succ(x0), Zero)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT2(zzz3520, zzz3521, zzz3522, zzz3523, Branch(zzz35240, zzz35241, zzz35242, zzz35243, zzz35244), zzz353, True, h, ba, bb) → new_splitGT2(zzz35240, zzz35241, zzz35242, zzz35243, zzz35244, zzz353, new_gt0(zzz353, zzz35240, h, ba), h, ba, bb)
new_splitGT2(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, False, h, ba, bb) → new_splitGT1(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, new_lt11(Right(zzz353), zzz3520, h, ba), h, ba, bb)
new_splitGT1(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, True, h, ba, bb) → new_splitGT(zzz3523, zzz353, h, ba, bb)
new_splitGT(Branch(zzz35240, zzz35241, zzz35242, zzz35243, zzz35244), zzz353, h, ba, bb) → new_splitGT2(zzz35240, zzz35241, zzz35242, zzz35243, zzz35244, zzz353, new_gt0(zzz353, zzz35240, h, ba), h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdb, bdc) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bdc), bdb, bdc)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dca)) → new_ltEs12(zzz2400, zzz220000, dca)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dbg, dbh) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(zzz5000, zzz4000, chg, chh, daa)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, deb), dec)) → new_compare5(zzz24000, zzz2200000, deb, dec)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdb, bdc) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdb), bdb, bdc)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Maybe, dac)) → new_esEs5(zzz5000, zzz4000, dac)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, ccf)) → new_ltEs5(zzz24001, zzz2200001, ccf)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgd)) → new_ltEs5(zzz24002, zzz2200002, bgd)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cec), cda)) → new_ltEs16(zzz2400, zzz220000, cec, cda)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_lt4(zzz24001, zzz2200001, beh, bfa)
new_primCompAux0(zzz24000, zzz2200000, zzz257, ccg) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, ccg))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgf)) → new_ltEs12(zzz24000, zzz2200000, bgf)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cda) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_lt18(zzz24000, zzz2200000, cag, cah, cba)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cac)) → new_lt6(zzz24000, zzz2200000, cac)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbe)) → new_esEs20(zzz5000, zzz4000, dbe)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bbg) → new_asAs(new_esEs23(zzz5000, zzz4000, bbg), new_esEs18(zzz5001, zzz4001, bbg))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, bhg)) → new_ltEs5(zzz24000, zzz2200000, bhg)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cff) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cda) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, gg) → new_esEs8(new_compare9(zzz24000, zzz2200000, gg), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), ccg) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, ccg), ccg)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbf)) → new_esEs5(zzz5000, zzz4000, dbf)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhb), bhc), bhd)) → new_ltEs10(zzz24000, zzz2200000, bhb, bhc, bhd)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfc)) → new_ltEs12(zzz24002, zzz2200002, bfc)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_[], ced)) → new_ltEs12(zzz24000, zzz2200000, ced)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, ded)) → new_compare9(zzz24000, zzz2200000, ded)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), caa, cab) → new_pePe(new_lt20(zzz24000, zzz2200000, caa), new_asAs(new_esEs28(zzz24000, zzz2200000, caa), new_ltEs19(zzz24001, zzz2200001, cab)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cff) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_esEs7(zzz24001, zzz2200001, beh, bfa)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_esEs4(zzz24001, zzz2200001, beb, bec)
new_esEs18(:(zzz5000, zzz5001), [], bbg) → False
new_esEs18([], :(zzz4000, zzz4001), bbg) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, bad), bae)) → new_esEs4(zzz5001, zzz4001, bad, bae)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bge) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bge)) → new_ltEs17(zzz2400, zzz220000, bge)
new_gt0(zzz353, zzz359, h, ba) → new_esEs8(new_compare19(Right(zzz353), zzz359, h, ba), GT)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdd), cda) → new_ltEs17(zzz24000, zzz2200000, cdd)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], ccg)) → new_ltEs12(zzz2400, zzz220000, ccg)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, caa), cab)) → new_ltEs7(zzz2400, zzz220000, caa, cab)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_@2, chd), che)) → new_esEs7(zzz5000, zzz4000, chd, che)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_lt9(zzz24000, zzz2200000, cbd)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], ccg) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_@2, cfc), cfd)) → new_ltEs7(zzz24000, zzz2200000, cfc, cfd)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bea)) → new_esEs18(zzz24001, zzz2200001, bea)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcd)) → new_ltEs17(zzz2400, zzz220000, dcd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, baf), bag)) → new_esEs7(zzz5001, zzz4001, baf, bag)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dbg, dbh) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bgg), bgh)) → new_ltEs16(zzz24000, zzz2200000, bgg, bgh)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cgg), cff) → new_esEs20(zzz5000, zzz4000, cgg)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bah)) → new_esEs18(zzz5001, zzz4001, bah)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cda) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_Either, chb), chc)) → new_esEs4(zzz5000, zzz4000, chb, chc)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bch)) → new_esEs20(zzz5000, zzz4000, bch)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs6(zzz5001, zzz4001, bba, bbb, bbc)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cfg), cfh), cff) → new_esEs4(zzz5000, zzz4000, cfg, cfh)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Ratio, dab)) → new_esEs20(zzz5000, zzz4000, dab)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cff) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_lt17(zzz24001, zzz2200001, bed)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cff) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hf)) → new_esEs18(zzz5000, zzz4000, hf)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bhh) → new_asAs(new_esEs26(zzz5000, zzz4000, bhh), new_esEs27(zzz5001, zzz4001, bhh))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hd), he)) → new_esEs7(zzz5000, zzz4000, hd, he)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hb), hc)) → new_esEs4(zzz5000, zzz4000, hb, hc)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_Either, cee), cef)) → new_ltEs16(zzz24000, zzz2200000, cee, cef)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbf)) → new_ltEs5(zzz2400, zzz220000, bbf)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbd)) → new_esEs20(zzz5001, zzz4001, bbd)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bab)) → new_esEs20(zzz5000, zzz4000, bab)
new_compare32(zzz24000, zzz2200000, app(ty_[], ddc)) → new_compare0(zzz24000, zzz2200000, ddc)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_lt11(zzz24000, zzz2200000, bdg, bdh)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_esEs7(zzz24000, zzz2200000, cbb, cbc)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cda) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cda) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cff) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_esEs5(zzz24001, zzz2200001, bed)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cff) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddb)) → new_ltEs5(zzz2400, zzz220000, ddb)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdd, bde, bdf) → new_pePe(new_lt13(zzz24000, zzz2200000, bdd), new_asAs(new_esEs24(zzz24000, zzz2200000, bdd), new_pePe(new_lt12(zzz24001, zzz2200001, bde), new_asAs(new_esEs25(zzz24001, zzz2200001, bde), new_ltEs11(zzz24002, zzz2200002, bdf)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cda) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(app(ty_@3, ceh), cfa), cfb)) → new_ltEs10(zzz24000, zzz2200000, ceh, cfa, cfb)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_lt4(zzz24000, zzz2200000, cbb, cbc)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Maybe, ceg)) → new_ltEs17(zzz24000, zzz2200000, ceg)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_lt9(zzz24001, zzz2200001, bfb)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, ccg) → new_fsEs(new_compare0(zzz2400, zzz220000, ccg))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, cdh), cea), cda) → new_ltEs7(zzz24000, zzz2200000, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), gh, ha) → new_asAs(new_esEs21(zzz5000, zzz4000, gh), new_esEs22(zzz5001, zzz4001, ha))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_[], chf)) → new_esEs18(zzz5000, zzz4000, chf)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cec, cda) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbe)) → new_ltEs12(zzz24001, zzz2200001, cbe)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cda) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_lt17(zzz24000, zzz2200000, caf)
new_compare0(:(zzz24000, zzz24001), [], ccg) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cff) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare26(zzz24000, zzz2200000, ddg, ddh, dea)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_lt9(zzz24000, zzz2200000, gg)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_lt18(zzz24001, zzz2200001, bee, bef, beg)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bfg), bfh), bga)) → new_ltEs10(zzz24002, zzz2200002, bfg, bfh, bga)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bbh), bca)) → new_esEs4(zzz5000, zzz4000, bbh, bca)
new_ltEs17(Nothing, Just(zzz2200000), bge) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_esEs6(zzz24000, zzz2200000, cag, cah, cba)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_esEs4(zzz24000, zzz2200000, bdg, bdh)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, dch), dda)) → new_ltEs7(zzz2400, zzz220000, dch, dda)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bge) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_lt11(zzz24000, zzz2200000, cad, cae)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_lt11(zzz24001, zzz2200001, beb, bec)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, cbh)) → new_ltEs17(zzz24001, zzz2200001, cbh)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cch), cda) → new_ltEs12(zzz24000, zzz2200000, cch)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs6(zzz5000, zzz4000, dbb, dbc, dbd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cac)) → new_esEs18(zzz24000, zzz2200000, cac)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccd), cce)) → new_ltEs7(zzz24001, zzz2200001, ccd, cce)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddf)) → new_compare31(zzz24000, zzz2200000, ddf)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bbg) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs6(zzz5000, zzz4000, bce, bcf, bcg)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddd), dde)) → new_compare19(zzz24000, zzz2200000, ddd, dde)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcb), bcc)) → new_esEs7(zzz5000, zzz4000, bcb, bcc)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, cgh), cff) → new_esEs5(zzz5000, zzz4000, cgh)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_esEs4(zzz24000, zzz2200000, cad, cae)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdb, bdc) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bda)) → new_esEs5(zzz5000, zzz4000, bda)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_esEs6(zzz24001, zzz2200001, bee, bef, beg)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cgc), cff) → new_esEs18(zzz5000, zzz4000, cgc)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdb, bdc) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgb), bgc)) → new_ltEs7(zzz24002, zzz2200002, bgb, bgc)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), dad) → False
new_esEs5(Just(zzz5000), Nothing, dad) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cec, cda) → False
new_compare211(zzz240, zzz22000, True, bdb, bdc) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cga), cgb), cff) → new_esEs7(zzz5000, zzz4000, cga, cgb)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_esEs20(zzz24000, zzz2200000, cbd)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Ratio, cfe)) → new_ltEs5(zzz24000, zzz2200000, cfe)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cda) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhe), bhf)) → new_ltEs7(zzz24000, zzz2200000, bhe, bhf)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, dad) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_esEs5(zzz24000, zzz2200000, caf)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bfd), bfe)) → new_ltEs16(zzz24002, zzz2200002, bfd, bfe)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs10(zzz2400, zzz220000, dce, dcf, dcg)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bha)) → new_ltEs17(zzz24000, zzz2200000, bha)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbe)) → new_esEs5(zzz5001, zzz4001, bbe)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bac)) → new_esEs5(zzz5000, zzz4000, bac)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), ccg) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, hg), hh), baa)) → new_esEs6(zzz5000, zzz4000, hg, hh, baa)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), cha, cff) → False
new_esEs4(Left(zzz5000), Right(zzz4000), cha, cff) → False
new_lt11(zzz240, zzz22000, bdb, bdc) → new_esEs8(new_compare19(zzz240, zzz22000, bdb, bdc), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dag), dah)) → new_esEs7(zzz5000, zzz4000, dag, dah)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgd), cge), cgf), cff) → new_esEs6(zzz5000, zzz4000, cgd, cge, cgf)
new_lt12(zzz24001, zzz2200001, app(ty_[], bea)) → new_lt6(zzz24001, zzz2200001, bea)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdb, bdc) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdb, bdc), bdb, bdc)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdb), cdc), cda) → new_ltEs16(zzz24000, zzz2200000, cdb, cdc)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_esEs20(zzz24000, zzz2200000, gg)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs10(zzz2400, zzz220000, bdd, bde, bdf)
new_ltEs5(zzz2400, zzz220000, bbf) → new_fsEs(new_compare9(zzz2400, zzz220000, bbf))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, cca), ccb), ccc)) → new_ltEs10(zzz24001, zzz2200001, cca, ccb, ccc)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cff) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bff)) → new_ltEs17(zzz24002, zzz2200002, bff)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcd)) → new_esEs18(zzz5000, zzz4000, bcd)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ceb), cda) → new_ltEs5(zzz24000, zzz2200000, ceb)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbf), cbg)) → new_ltEs16(zzz24001, zzz2200001, cbf, cbg)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dba)) → new_esEs18(zzz5000, zzz4000, dba)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcb), dcc)) → new_ltEs16(zzz2400, zzz220000, dcb, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dae), daf)) → new_esEs4(zzz5000, zzz4000, dae, daf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cde), cdf), cdg), cda) → new_ltEs10(zzz24000, zzz2200000, cde, cdf, cdg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_esEs20(zzz24001, zzz2200001, bfb)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_sr(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_compare30(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs15(x0, x1)
new_esEs10(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(True, False)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs9(x0, x1, ty_Float)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_compare211(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs18([], :(x0, x1), x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Nothing, Nothing, x0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Float)
new_ltEs12(x0, x1, x2)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs28(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_compare28(x0, x1, True)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_compare0(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18([], [], x0)
new_compare32(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs15(Char(x0), Char(x1))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt15(x0, x1)
new_fsEs(x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs17(Nothing, Just(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare25(x0, x1, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs9(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare0([], [], x0)
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_lt7(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Integer)
new_lt12(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Float)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_ltEs17(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs11(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1)
new_ltEs13(x0, x1)
new_esEs11(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Integer)
new_lt9(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, x2, x3)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_gt0(x0, x1, x2, x3)
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(False, False)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt13(x0, x1, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(False, False)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1)
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Float)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Bool)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, True, x2, x3)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Just(x0), x1)
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Char)
new_compare110(x0, x1, False, x2, x3)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt12(x0, x1, ty_Bool)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs21(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT(Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz353, h, ba, bb) → new_splitLT2(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz353, new_lt11(Right(zzz353), zzz35130, h, ba), h, ba, bb)
new_splitLT2(zzz3510, zzz3511, zzz3512, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz3514, zzz353, True, h, ba, bb) → new_splitLT2(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz353, new_lt11(Right(zzz353), zzz35130, h, ba), h, ba, bb)
new_splitLT2(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, False, h, ba, bb) → new_splitLT1(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, new_gt0(zzz353, zzz3510, h, ba), h, ba, bb)
new_splitLT1(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, True, h, ba, bb) → new_splitLT(zzz3514, zzz353, h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdb, bdc) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bdc), bdb, bdc)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dca)) → new_ltEs12(zzz2400, zzz220000, dca)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dbg, dbh) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(zzz5000, zzz4000, chg, chh, daa)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, deb), dec)) → new_compare5(zzz24000, zzz2200000, deb, dec)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdb, bdc) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdb), bdb, bdc)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Maybe, dac)) → new_esEs5(zzz5000, zzz4000, dac)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, ccf)) → new_ltEs5(zzz24001, zzz2200001, ccf)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgd)) → new_ltEs5(zzz24002, zzz2200002, bgd)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cec), cda)) → new_ltEs16(zzz2400, zzz220000, cec, cda)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_lt4(zzz24001, zzz2200001, beh, bfa)
new_primCompAux0(zzz24000, zzz2200000, zzz257, ccg) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, ccg))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgf)) → new_ltEs12(zzz24000, zzz2200000, bgf)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cda) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_lt18(zzz24000, zzz2200000, cag, cah, cba)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cac)) → new_lt6(zzz24000, zzz2200000, cac)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbe)) → new_esEs20(zzz5000, zzz4000, dbe)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bbg) → new_asAs(new_esEs23(zzz5000, zzz4000, bbg), new_esEs18(zzz5001, zzz4001, bbg))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, bhg)) → new_ltEs5(zzz24000, zzz2200000, bhg)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cff) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cda) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, gg) → new_esEs8(new_compare9(zzz24000, zzz2200000, gg), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), ccg) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, ccg), ccg)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbf)) → new_esEs5(zzz5000, zzz4000, dbf)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhb), bhc), bhd)) → new_ltEs10(zzz24000, zzz2200000, bhb, bhc, bhd)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfc)) → new_ltEs12(zzz24002, zzz2200002, bfc)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_[], ced)) → new_ltEs12(zzz24000, zzz2200000, ced)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, ded)) → new_compare9(zzz24000, zzz2200000, ded)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), caa, cab) → new_pePe(new_lt20(zzz24000, zzz2200000, caa), new_asAs(new_esEs28(zzz24000, zzz2200000, caa), new_ltEs19(zzz24001, zzz2200001, cab)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cff) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_esEs7(zzz24001, zzz2200001, beh, bfa)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_esEs4(zzz24001, zzz2200001, beb, bec)
new_esEs18(:(zzz5000, zzz5001), [], bbg) → False
new_esEs18([], :(zzz4000, zzz4001), bbg) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, bad), bae)) → new_esEs4(zzz5001, zzz4001, bad, bae)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bge) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bge)) → new_ltEs17(zzz2400, zzz220000, bge)
new_gt0(zzz353, zzz359, h, ba) → new_esEs8(new_compare19(Right(zzz353), zzz359, h, ba), GT)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdd), cda) → new_ltEs17(zzz24000, zzz2200000, cdd)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], ccg)) → new_ltEs12(zzz2400, zzz220000, ccg)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, caa), cab)) → new_ltEs7(zzz2400, zzz220000, caa, cab)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_@2, chd), che)) → new_esEs7(zzz5000, zzz4000, chd, che)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_lt9(zzz24000, zzz2200000, cbd)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], ccg) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_@2, cfc), cfd)) → new_ltEs7(zzz24000, zzz2200000, cfc, cfd)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bea)) → new_esEs18(zzz24001, zzz2200001, bea)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcd)) → new_ltEs17(zzz2400, zzz220000, dcd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, baf), bag)) → new_esEs7(zzz5001, zzz4001, baf, bag)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dbg, dbh) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bgg), bgh)) → new_ltEs16(zzz24000, zzz2200000, bgg, bgh)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cgg), cff) → new_esEs20(zzz5000, zzz4000, cgg)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bah)) → new_esEs18(zzz5001, zzz4001, bah)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cda) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_Either, chb), chc)) → new_esEs4(zzz5000, zzz4000, chb, chc)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bch)) → new_esEs20(zzz5000, zzz4000, bch)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs6(zzz5001, zzz4001, bba, bbb, bbc)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cfg), cfh), cff) → new_esEs4(zzz5000, zzz4000, cfg, cfh)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Ratio, dab)) → new_esEs20(zzz5000, zzz4000, dab)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cff) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_lt17(zzz24001, zzz2200001, bed)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cff) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hf)) → new_esEs18(zzz5000, zzz4000, hf)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bhh) → new_asAs(new_esEs26(zzz5000, zzz4000, bhh), new_esEs27(zzz5001, zzz4001, bhh))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hd), he)) → new_esEs7(zzz5000, zzz4000, hd, he)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hb), hc)) → new_esEs4(zzz5000, zzz4000, hb, hc)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_Either, cee), cef)) → new_ltEs16(zzz24000, zzz2200000, cee, cef)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbf)) → new_ltEs5(zzz2400, zzz220000, bbf)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbd)) → new_esEs20(zzz5001, zzz4001, bbd)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bab)) → new_esEs20(zzz5000, zzz4000, bab)
new_compare32(zzz24000, zzz2200000, app(ty_[], ddc)) → new_compare0(zzz24000, zzz2200000, ddc)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_lt11(zzz24000, zzz2200000, bdg, bdh)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_esEs7(zzz24000, zzz2200000, cbb, cbc)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cda) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cda) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cff) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_esEs5(zzz24001, zzz2200001, bed)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cff) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddb)) → new_ltEs5(zzz2400, zzz220000, ddb)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdd, bde, bdf) → new_pePe(new_lt13(zzz24000, zzz2200000, bdd), new_asAs(new_esEs24(zzz24000, zzz2200000, bdd), new_pePe(new_lt12(zzz24001, zzz2200001, bde), new_asAs(new_esEs25(zzz24001, zzz2200001, bde), new_ltEs11(zzz24002, zzz2200002, bdf)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cda) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(app(ty_@3, ceh), cfa), cfb)) → new_ltEs10(zzz24000, zzz2200000, ceh, cfa, cfb)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_lt4(zzz24000, zzz2200000, cbb, cbc)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Maybe, ceg)) → new_ltEs17(zzz24000, zzz2200000, ceg)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_lt9(zzz24001, zzz2200001, bfb)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, ccg) → new_fsEs(new_compare0(zzz2400, zzz220000, ccg))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, cdh), cea), cda) → new_ltEs7(zzz24000, zzz2200000, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), gh, ha) → new_asAs(new_esEs21(zzz5000, zzz4000, gh), new_esEs22(zzz5001, zzz4001, ha))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_[], chf)) → new_esEs18(zzz5000, zzz4000, chf)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cec, cda) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbe)) → new_ltEs12(zzz24001, zzz2200001, cbe)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cda) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_lt17(zzz24000, zzz2200000, caf)
new_compare0(:(zzz24000, zzz24001), [], ccg) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cff) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare26(zzz24000, zzz2200000, ddg, ddh, dea)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_lt9(zzz24000, zzz2200000, gg)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_lt18(zzz24001, zzz2200001, bee, bef, beg)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bfg), bfh), bga)) → new_ltEs10(zzz24002, zzz2200002, bfg, bfh, bga)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bbh), bca)) → new_esEs4(zzz5000, zzz4000, bbh, bca)
new_ltEs17(Nothing, Just(zzz2200000), bge) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_esEs6(zzz24000, zzz2200000, cag, cah, cba)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_esEs4(zzz24000, zzz2200000, bdg, bdh)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, dch), dda)) → new_ltEs7(zzz2400, zzz220000, dch, dda)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bge) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_lt11(zzz24000, zzz2200000, cad, cae)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_lt11(zzz24001, zzz2200001, beb, bec)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, cbh)) → new_ltEs17(zzz24001, zzz2200001, cbh)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cch), cda) → new_ltEs12(zzz24000, zzz2200000, cch)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs6(zzz5000, zzz4000, dbb, dbc, dbd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cac)) → new_esEs18(zzz24000, zzz2200000, cac)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccd), cce)) → new_ltEs7(zzz24001, zzz2200001, ccd, cce)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddf)) → new_compare31(zzz24000, zzz2200000, ddf)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bbg) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs6(zzz5000, zzz4000, bce, bcf, bcg)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddd), dde)) → new_compare19(zzz24000, zzz2200000, ddd, dde)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcb), bcc)) → new_esEs7(zzz5000, zzz4000, bcb, bcc)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, cgh), cff) → new_esEs5(zzz5000, zzz4000, cgh)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_esEs4(zzz24000, zzz2200000, cad, cae)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdb, bdc) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bda)) → new_esEs5(zzz5000, zzz4000, bda)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_esEs6(zzz24001, zzz2200001, bee, bef, beg)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cgc), cff) → new_esEs18(zzz5000, zzz4000, cgc)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdb, bdc) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgb), bgc)) → new_ltEs7(zzz24002, zzz2200002, bgb, bgc)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), dad) → False
new_esEs5(Just(zzz5000), Nothing, dad) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cec, cda) → False
new_compare211(zzz240, zzz22000, True, bdb, bdc) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cga), cgb), cff) → new_esEs7(zzz5000, zzz4000, cga, cgb)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_esEs20(zzz24000, zzz2200000, cbd)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Ratio, cfe)) → new_ltEs5(zzz24000, zzz2200000, cfe)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cda) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhe), bhf)) → new_ltEs7(zzz24000, zzz2200000, bhe, bhf)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, dad) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_esEs5(zzz24000, zzz2200000, caf)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bfd), bfe)) → new_ltEs16(zzz24002, zzz2200002, bfd, bfe)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs10(zzz2400, zzz220000, dce, dcf, dcg)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bha)) → new_ltEs17(zzz24000, zzz2200000, bha)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbe)) → new_esEs5(zzz5001, zzz4001, bbe)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bac)) → new_esEs5(zzz5000, zzz4000, bac)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), ccg) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, hg), hh), baa)) → new_esEs6(zzz5000, zzz4000, hg, hh, baa)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), cha, cff) → False
new_esEs4(Left(zzz5000), Right(zzz4000), cha, cff) → False
new_lt11(zzz240, zzz22000, bdb, bdc) → new_esEs8(new_compare19(zzz240, zzz22000, bdb, bdc), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dag), dah)) → new_esEs7(zzz5000, zzz4000, dag, dah)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgd), cge), cgf), cff) → new_esEs6(zzz5000, zzz4000, cgd, cge, cgf)
new_lt12(zzz24001, zzz2200001, app(ty_[], bea)) → new_lt6(zzz24001, zzz2200001, bea)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdb, bdc) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdb, bdc), bdb, bdc)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdb), cdc), cda) → new_ltEs16(zzz24000, zzz2200000, cdb, cdc)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_esEs20(zzz24000, zzz2200000, gg)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs10(zzz2400, zzz220000, bdd, bde, bdf)
new_ltEs5(zzz2400, zzz220000, bbf) → new_fsEs(new_compare9(zzz2400, zzz220000, bbf))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, cca), ccb), ccc)) → new_ltEs10(zzz24001, zzz2200001, cca, ccb, ccc)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cff) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bff)) → new_ltEs17(zzz24002, zzz2200002, bff)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcd)) → new_esEs18(zzz5000, zzz4000, bcd)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ceb), cda) → new_ltEs5(zzz24000, zzz2200000, ceb)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbf), cbg)) → new_ltEs16(zzz24001, zzz2200001, cbf, cbg)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dba)) → new_esEs18(zzz5000, zzz4000, dba)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcb), dcc)) → new_ltEs16(zzz2400, zzz220000, dcb, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dae), daf)) → new_esEs4(zzz5000, zzz4000, dae, daf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cde), cdf), cdg), cda) → new_ltEs10(zzz24000, zzz2200000, cde, cdf, cdg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_esEs20(zzz24001, zzz2200001, bfb)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_sr(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_compare30(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs15(x0, x1)
new_esEs10(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(True, False)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs9(x0, x1, ty_Float)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_compare211(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs18([], :(x0, x1), x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Nothing, Nothing, x0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Float)
new_ltEs12(x0, x1, x2)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs28(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_compare28(x0, x1, True)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_compare0(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18([], [], x0)
new_compare32(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs15(Char(x0), Char(x1))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt15(x0, x1)
new_fsEs(x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs17(Nothing, Just(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare25(x0, x1, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs9(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare0([], [], x0)
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_lt7(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Integer)
new_lt12(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Float)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_ltEs17(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs11(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1)
new_ltEs13(x0, x1)
new_esEs11(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Integer)
new_lt9(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, x2, x3)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_gt0(x0, x1, x2, x3)
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(False, False)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt13(x0, x1, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(False, False)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1)
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Float)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Bool)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, True, x2, x3)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Just(x0), x1)
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Char)
new_compare110(x0, x1, False, x2, x3)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt12(x0, x1, ty_Bool)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs21(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT0(Branch(zzz31640, zzz31641, zzz31642, zzz31643, zzz31644), zzz317, h, ba, bb) → new_splitGT20(zzz31640, zzz31641, zzz31642, zzz31643, zzz31644, zzz317, new_gt(Left(zzz317), zzz31640, h, ba), h, ba, bb)
new_splitGT20(zzz3160, zzz3161, zzz3162, zzz3163, Branch(zzz31640, zzz31641, zzz31642, zzz31643, zzz31644), zzz317, True, h, ba, bb) → new_splitGT20(zzz31640, zzz31641, zzz31642, zzz31643, zzz31644, zzz317, new_gt(Left(zzz317), zzz31640, h, ba), h, ba, bb)
new_splitGT10(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, True, h, ba, bb) → new_splitGT0(zzz3163, zzz317, h, ba, bb)
new_splitGT20(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, False, h, ba, bb) → new_splitGT10(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, new_lt11(Left(zzz317), zzz3160, h, ba), h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdd, bde) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bde), bdd, bde)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dcc)) → new_ltEs12(zzz2400, zzz220000, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dca, dcb) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(zzz5000, zzz4000, daa, dab, dac)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, ded), dee)) → new_compare5(zzz24000, zzz2200000, ded, dee)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdd, bde) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdd), bdd, bde)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Maybe, dae)) → new_esEs5(zzz5000, zzz4000, dae)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, cch)) → new_ltEs5(zzz24001, zzz2200001, cch)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgf)) → new_ltEs5(zzz24002, zzz2200002, bgf)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cee), cdc)) → new_ltEs16(zzz2400, zzz220000, cee, cdc)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_lt4(zzz24001, zzz2200001, bfb, bfc)
new_primCompAux0(zzz24000, zzz2200000, zzz257, cda) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, cda))
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgh)) → new_ltEs12(zzz24000, zzz2200000, bgh)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cdc) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt18(zzz24000, zzz2200000, cba, cbb, cbc)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cae)) → new_lt6(zzz24000, zzz2200000, cae)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbg)) → new_esEs20(zzz5000, zzz4000, dbg)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bca) → new_asAs(new_esEs23(zzz5000, zzz4000, bca), new_esEs18(zzz5001, zzz4001, bca))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, caa)) → new_ltEs5(zzz24000, zzz2200000, caa)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cfh) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cdc) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, ha) → new_esEs8(new_compare9(zzz24000, zzz2200000, ha), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), cda) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, cda), cda)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbh)) → new_esEs5(zzz5000, zzz4000, dbh)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_ltEs10(zzz24000, zzz2200000, bhd, bhe, bhf)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfe)) → new_ltEs12(zzz24002, zzz2200002, bfe)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_[], cef)) → new_ltEs12(zzz24000, zzz2200000, cef)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, def)) → new_compare9(zzz24000, zzz2200000, def)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), cac, cad) → new_pePe(new_lt20(zzz24000, zzz2200000, cac), new_asAs(new_esEs28(zzz24000, zzz2200000, cac), new_ltEs19(zzz24001, zzz2200001, cad)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cfh) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, bfb), bfc)) → new_esEs7(zzz24001, zzz2200001, bfb, bfc)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_esEs4(zzz24001, zzz2200001, bed, bee)
new_esEs18(:(zzz5000, zzz5001), [], bca) → False
new_esEs18([], :(zzz4000, zzz4001), bca) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, baf), bag)) → new_esEs4(zzz5001, zzz4001, baf, bag)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bgg) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bgg)) → new_ltEs17(zzz2400, zzz220000, bgg)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdf), cdc) → new_ltEs17(zzz24000, zzz2200000, cdf)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], cda)) → new_ltEs12(zzz2400, zzz220000, cda)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, cac), cad)) → new_ltEs7(zzz2400, zzz220000, cac, cad)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_@2, chf), chg)) → new_esEs7(zzz5000, zzz4000, chf, chg)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_lt9(zzz24000, zzz2200000, cbf)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], cda) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_@2, cfe), cff)) → new_ltEs7(zzz24000, zzz2200000, cfe, cff)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bec)) → new_esEs18(zzz24001, zzz2200001, bec)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcf)) → new_ltEs17(zzz2400, zzz220000, dcf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, bah), bba)) → new_esEs7(zzz5001, zzz4001, bah, bba)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dca, dcb) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bha), bhb)) → new_ltEs16(zzz24000, zzz2200000, bha, bhb)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cha), cfh) → new_esEs20(zzz5000, zzz4000, cha)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bbb)) → new_esEs18(zzz5001, zzz4001, bbb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cdc) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(app(ty_Either, chd), che)) → new_esEs4(zzz5000, zzz4000, chd, che)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bdb)) → new_esEs20(zzz5000, zzz4000, bdb)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(zzz5001, zzz4001, bbc, bbd, bbe)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cga), cgb), cfh) → new_esEs4(zzz5000, zzz4000, cga, cgb)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_Ratio, dad)) → new_esEs20(zzz5000, zzz4000, dad)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cfh) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_lt17(zzz24001, zzz2200001, bef)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cfh) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hh)) → new_esEs18(zzz5000, zzz4000, hh)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cab) → new_asAs(new_esEs26(zzz5000, zzz4000, cab), new_esEs27(zzz5001, zzz4001, cab))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hf), hg)) → new_esEs7(zzz5000, zzz4000, hf, hg)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hd), he)) → new_esEs4(zzz5000, zzz4000, hd, he)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(ty_Either, ceg), ceh)) → new_ltEs16(zzz24000, zzz2200000, ceg, ceh)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbh)) → new_ltEs5(zzz2400, zzz220000, bbh)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbf)) → new_esEs20(zzz5001, zzz4001, bbf)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bad)) → new_esEs20(zzz5000, zzz4000, bad)
new_compare32(zzz24000, zzz2200000, app(ty_[], dde)) → new_compare0(zzz24000, zzz2200000, dde)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_lt11(zzz24000, zzz2200000, bea, beb)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_esEs7(zzz24000, zzz2200000, cbd, cbe)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cdc) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cdc) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cfh) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bef)) → new_esEs5(zzz24001, zzz2200001, bef)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cfh) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddd)) → new_ltEs5(zzz2400, zzz220000, ddd)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdf, bdg, bdh) → new_pePe(new_lt13(zzz24000, zzz2200000, bdf), new_asAs(new_esEs24(zzz24000, zzz2200000, bdf), new_pePe(new_lt12(zzz24001, zzz2200001, bdg), new_asAs(new_esEs25(zzz24001, zzz2200001, bdg), new_ltEs11(zzz24002, zzz2200002, bdh)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cdc) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs10(zzz24000, zzz2200000, cfb, cfc, cfd)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbd), cbe)) → new_lt4(zzz24000, zzz2200000, cbd, cbe)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Maybe, cfa)) → new_ltEs17(zzz24000, zzz2200000, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_lt9(zzz24001, zzz2200001, bfd)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, cda) → new_fsEs(new_compare0(zzz2400, zzz220000, cda))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, ceb), cec), cdc) → new_ltEs7(zzz24000, zzz2200000, ceb, cec)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), hb, hc) → new_asAs(new_esEs21(zzz5000, zzz4000, hb), new_esEs22(zzz5001, zzz4001, hc))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, app(ty_[], chh)) → new_esEs18(zzz5000, zzz4000, chh)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cee, cdc) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbg)) → new_ltEs12(zzz24001, zzz2200001, cbg)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cdc) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_lt17(zzz24000, zzz2200000, cah)
new_compare0(:(zzz24000, zzz24001), [], cda) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cfh) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, dea), deb), dec)) → new_compare26(zzz24000, zzz2200000, dea, deb, dec)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_lt9(zzz24000, zzz2200000, ha)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_lt18(zzz24001, zzz2200001, beg, beh, bfa)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bga), bgb), bgc)) → new_ltEs10(zzz24002, zzz2200002, bga, bgb, bgc)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bcb), bcc)) → new_esEs4(zzz5000, zzz4000, bcb, bcc)
new_ltEs17(Nothing, Just(zzz2200000), bgg) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(zzz24000, zzz2200000, cba, cbb, cbc)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bea), beb)) → new_esEs4(zzz24000, zzz2200000, bea, beb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, ddb), ddc)) → new_ltEs7(zzz2400, zzz220000, ddb, ddc)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bgg) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_lt11(zzz24000, zzz2200000, caf, cag)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, bed), bee)) → new_lt11(zzz24001, zzz2200001, bed, bee)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, ccb)) → new_ltEs17(zzz24001, zzz2200001, ccb)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cdb), cdc) → new_ltEs12(zzz24000, zzz2200000, cdb)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs6(zzz5000, zzz4000, dbd, dbe, dbf)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cae)) → new_esEs18(zzz24000, zzz2200000, cae)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccf), ccg)) → new_ltEs7(zzz24001, zzz2200001, ccf, ccg)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_gt(zzz3510, zzz4870, gg, gh) → new_esEs8(new_compare19(zzz3510, zzz4870, gg, gh), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddh)) → new_compare31(zzz24000, zzz2200000, ddh)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bca) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zzz5000, zzz4000, bcg, bch, bda)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddf), ddg)) → new_compare19(zzz24000, zzz2200000, ddf, ddg)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcd), bce)) → new_esEs7(zzz5000, zzz4000, bcd, bce)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, chb), cfh) → new_esEs5(zzz5000, zzz4000, chb)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, caf), cag)) → new_esEs4(zzz24000, zzz2200000, caf, cag)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdd, bde) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bdc)) → new_esEs5(zzz5000, zzz4000, bdc)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zzz24001, zzz2200001, beg, beh, bfa)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cge), cfh) → new_esEs18(zzz5000, zzz4000, cge)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdd, bde) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgd), bge)) → new_ltEs7(zzz24002, zzz2200002, bgd, bge)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), daf) → False
new_esEs5(Just(zzz5000), Nothing, daf) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cee, cdc) → False
new_compare211(zzz240, zzz22000, True, bdd, bde) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cgc), cgd), cfh) → new_esEs7(zzz5000, zzz4000, cgc, cgd)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbf)) → new_esEs20(zzz24000, zzz2200000, cbf)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, app(ty_Ratio, cfg)) → new_ltEs5(zzz24000, zzz2200000, cfg)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cee, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cdc) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhg), bhh)) → new_ltEs7(zzz24000, zzz2200000, bhg, bhh)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, daf) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, cah)) → new_esEs5(zzz24000, zzz2200000, cah)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), chc, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bff), bfg)) → new_ltEs16(zzz24002, zzz2200002, bff, bfg)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dcg), dch), dda)) → new_ltEs10(zzz2400, zzz220000, dcg, dch, dda)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bhc)) → new_ltEs17(zzz24000, zzz2200000, bhc)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbg)) → new_esEs5(zzz5001, zzz4001, bbg)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bae)) → new_esEs5(zzz5000, zzz4000, bae)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), cda) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(zzz5000, zzz4000, baa, bab, bac)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), chc, cfh) → False
new_esEs4(Left(zzz5000), Right(zzz4000), chc, cfh) → False
new_lt11(zzz240, zzz22000, bdd, bde) → new_esEs8(new_compare19(zzz240, zzz22000, bdd, bde), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dba), dbb)) → new_esEs7(zzz5000, zzz4000, dba, dbb)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgf), cgg), cgh), cfh) → new_esEs6(zzz5000, zzz4000, cgf, cgg, cgh)
new_lt12(zzz24001, zzz2200001, app(ty_[], bec)) → new_lt6(zzz24001, zzz2200001, bec)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdd, bde) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdd, bde), bdd, bde)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdd), cde), cdc) → new_ltEs16(zzz24000, zzz2200000, cdd, cde)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, ha)) → new_esEs20(zzz24000, zzz2200000, ha)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs10(zzz2400, zzz220000, bdf, bdg, bdh)
new_ltEs5(zzz2400, zzz220000, bbh) → new_fsEs(new_compare9(zzz2400, zzz220000, bbh))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs10(zzz24001, zzz2200001, ccc, ccd, cce)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cfh) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bfh)) → new_ltEs17(zzz24002, zzz2200002, bfh)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcf)) → new_esEs18(zzz5000, zzz4000, bcf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ced), cdc) → new_ltEs5(zzz24000, zzz2200000, ced)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbh), cca)) → new_ltEs16(zzz24001, zzz2200001, cbh, cca)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dbc)) → new_esEs18(zzz5000, zzz4000, dbc)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcd), dce)) → new_ltEs16(zzz2400, zzz220000, dcd, dce)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dag), dah)) → new_esEs4(zzz5000, zzz4000, dag, dah)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cdg), cdh), cea), cdc) → new_ltEs10(zzz24000, zzz2200000, cdg, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfd)) → new_esEs20(zzz24001, zzz2200001, bfd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_lt12(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs5(x0, x1, x2)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_@0)
new_ltEs14(True, False)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Integer)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True)
new_gt(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_@0)
new_esEs18([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs15(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt15(x0, x1)
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare32(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare25(x0, x1, True)
new_compare19(x0, x1, x2, x3)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_ltEs20(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs5(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Double)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt12(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18([], [], x0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare211(x0, x1, True, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(False, False)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Integer)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Int)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs12(x0, x1, x2)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1, x2)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt13(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_compare32(x0, x1, ty_Bool)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, True, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_@0)
new_compare32(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Integer)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_ltEs4(x0, x1)
new_ltEs17(Nothing, Nothing, x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_pePe(True, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs21(x0, x1, ty_@0)
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))

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

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



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

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

new_splitLT20(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, False, h, ba, bb) → new_splitLT10(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, new_gt1(zzz317, zzz3150, h, ba), h, ba, bb)
new_splitLT10(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, True, h, ba, bb) → new_splitLT0(zzz3154, zzz317, h, ba, bb)
new_splitLT0(Branch(zzz31530, zzz31531, zzz31532, zzz31533, zzz31534), zzz317, h, ba, bb) → new_splitLT20(zzz31530, zzz31531, zzz31532, zzz31533, zzz31534, zzz317, new_lt11(Left(zzz317), zzz31530, h, ba), h, ba, bb)
new_splitLT20(zzz3150, zzz3151, zzz3152, Branch(zzz31530, zzz31531, zzz31532, zzz31533, zzz31534), zzz3154, zzz317, True, h, ba, bb) → new_splitLT20(zzz31530, zzz31531, zzz31532, zzz31533, zzz31534, zzz317, new_lt11(Left(zzz317), zzz31530, h, ba), h, ba, bb)

The TRS R consists of the following rules:

new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, bdb, bdc) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, bdc), bdb, bdc)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], dca)) → new_ltEs12(zzz2400, zzz220000, dca)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dbg, dbh) → LT
new_lt18(zzz24000, zzz2200000, gd, ge, gf) → new_esEs8(new_compare26(zzz24000, zzz2200000, gd, ge, gf), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(zzz5000, zzz4000, chg, chh, daa)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, deb), dec)) → new_compare5(zzz24000, zzz2200000, deb, dec)
new_compare211(Left(zzz2400), Left(zzz220000), False, bdb, bdc) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, bdb), bdb, bdc)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Maybe, dac)) → new_esEs5(zzz5000, zzz4000, dac)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, ccf)) → new_ltEs5(zzz24001, zzz2200001, ccf)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, bgd)) → new_ltEs5(zzz24002, zzz2200002, bgd)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, cec), cda)) → new_ltEs16(zzz2400, zzz220000, cec, cda)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, fc), fd)) → new_esEs7(zzz5002, zzz4002, fc, fd)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_lt4(zzz24001, zzz2200001, beh, bfa)
new_primCompAux0(zzz24000, zzz2200000, zzz257, ccg) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, ccg))
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], bgf)) → new_ltEs12(zzz24000, zzz2200000, bgf)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_lt17(zzz24000, zzz2200000, bc)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, cda) → new_ltEs18(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_lt18(zzz24000, zzz2200000, cag, cah, cba)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(ty_[], cac)) → new_lt6(zzz24000, zzz2200000, cac)
new_ltEs14(False, True) → True
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dbe)) → new_esEs20(zzz5000, zzz4000, dbe)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bbg) → new_asAs(new_esEs23(zzz5000, zzz4000, bbg), new_esEs18(zzz5001, zzz4001, bbg))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, bhg)) → new_ltEs5(zzz24000, zzz2200000, bhg)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, cff) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, cda) → new_ltEs14(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, gg) → new_esEs8(new_compare9(zzz24000, zzz2200000, gg), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), ccg) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, ccg), ccg)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dbf)) → new_esEs5(zzz5000, zzz4000, dbf)
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_ltEs8(EQ, EQ) → True
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, bhb), bhc), bhd)) → new_ltEs10(zzz24000, zzz2200000, bhb, bhc, bhd)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bfc)) → new_ltEs12(zzz24002, zzz2200002, bfc)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_esEs12(@0, @0) → True
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, gb)) → new_esEs20(zzz5002, zzz4002, gb)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_[], ced)) → new_ltEs12(zzz24000, zzz2200000, ced)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, ded)) → new_compare9(zzz24000, zzz2200000, ded)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), caa, cab) → new_pePe(new_lt20(zzz24000, zzz2200000, caa), new_asAs(new_esEs28(zzz24000, zzz2200000, caa), new_ltEs19(zzz24001, zzz2200001, cab)))
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, cff) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare24(zzz24000, zzz2200000, False, bd, be) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_[], da)) → new_esEs18(zzz5000, zzz4000, da)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, eg)) → new_esEs20(zzz5001, zzz4001, eg)
new_pePe(False, zzz256) → zzz256
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, beh), bfa)) → new_esEs7(zzz24001, zzz2200001, beh, bfa)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_esEs4(zzz24001, zzz2200001, beb, bec)
new_esEs18(:(zzz5000, zzz5001), [], bbg) → False
new_esEs18([], :(zzz4000, zzz4001), bbg) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, bad), bae)) → new_esEs4(zzz5001, zzz4001, bad, bae)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, bge) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, bge)) → new_ltEs17(zzz2400, zzz220000, bge)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, cdd), cda) → new_ltEs17(zzz24000, zzz2200000, cdd)
new_compare10(zzz24000, zzz2200000, True, bc) → LT
new_ltEs20(zzz2400, zzz220000, app(ty_[], ccg)) → new_ltEs12(zzz2400, zzz220000, ccg)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, caa), cab)) → new_ltEs7(zzz2400, zzz220000, caa, cab)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_@2, chd), che)) → new_esEs7(zzz5000, zzz4000, chd, che)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zzz5002, zzz4002, fg, fh, ga)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_lt9(zzz24000, zzz2200000, cbd)
new_ltEs8(LT, EQ) → True
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_compare10(zzz24000, zzz2200000, False, bc) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, dg), dh)) → new_esEs4(zzz5001, zzz4001, dg, dh)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_compare0([], [], ccg) → EQ
new_pePe(True, zzz256) → True
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_@2, cfc), cfd)) → new_ltEs7(zzz24000, zzz2200000, cfc, cfd)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bea)) → new_esEs18(zzz24001, zzz2200001, bea)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, dcd)) → new_ltEs17(zzz2400, zzz220000, dcd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bh)) → new_esEs18(zzz24000, zzz2200000, bh)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, baf), bag)) → new_esEs7(zzz5001, zzz4001, baf, bag)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, bc) → new_esEs8(new_compare31(zzz24000, zzz2200000, bc), LT)
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_ltEs8(EQ, LT) → False
new_compare110(zzz242, zzz243, False, dbg, dbh) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, bgg), bgh)) → new_ltEs16(zzz24000, zzz2200000, bgg, bgh)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, gd, ge, gf) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cgg), cff) → new_esEs20(zzz5000, zzz4000, cgg)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_esEs7(zzz24000, zzz2200000, bd, be)
new_esEs8(GT, GT) → True
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_[], bah)) → new_esEs18(zzz5001, zzz4001, bah)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, cda) → new_ltEs4(zzz24000, zzz2200000)
new_compare210(zzz24000, zzz2200000, False, bc) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, bc), bc)
new_compare17(zzz24000, zzz2200000, True, bd, be) → LT
new_compare29(zzz24000, zzz2200000, True, gd, ge, gf) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(app(ty_Either, chb), chc)) → new_esEs4(zzz5000, zzz4000, chb, chc)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, bch)) → new_esEs20(zzz5000, zzz4000, bch)
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs6(zzz5001, zzz4001, bba, bbb, bbc)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, cfg), cfh), cff) → new_esEs4(zzz5000, zzz4000, cfg, cfh)
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_Ratio, dab)) → new_esEs20(zzz5000, zzz4000, dab)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], ec)) → new_esEs18(zzz5001, zzz4001, ec)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, cff) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_lt17(zzz24001, zzz2200001, bed)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, cff) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], hf)) → new_esEs18(zzz5000, zzz4000, hf)
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bhh) → new_asAs(new_esEs26(zzz5000, zzz4000, bhh), new_esEs27(zzz5001, zzz4001, bhh))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz24000, zzz2200000, gd, ge, gf)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, hd), he)) → new_esEs7(zzz5000, zzz4000, hd, he)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, hb), hc)) → new_esEs4(zzz5000, zzz4000, hb, hc)
new_compare24(zzz24000, zzz2200000, True, bd, be) → EQ
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(ty_Either, cee), cef)) → new_ltEs16(zzz24000, zzz2200000, cee, cef)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, bbf)) → new_ltEs5(zzz2400, zzz220000, bbf)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bbd)) → new_esEs20(zzz5001, zzz4001, bbd)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bab)) → new_esEs20(zzz5000, zzz4000, bab)
new_compare32(zzz24000, zzz2200000, app(ty_[], ddc)) → new_compare0(zzz24000, zzz2200000, ddc)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_lt11(zzz24000, zzz2200000, bdg, bdh)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_esEs7(zzz24000, zzz2200000, cbb, cbc)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_gt1(zzz317, zzz323, h, ba) → new_esEs8(new_compare19(Left(zzz317), zzz323, h, ba), GT)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, cda) → new_ltEs9(zzz24000, zzz2200000)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, cda) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, cff) → new_esEs17(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bed)) → new_esEs5(zzz24001, zzz2200001, bed)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, cf), cg)) → new_esEs7(zzz5000, zzz4000, cf, cg)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, cff) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ddb)) → new_ltEs5(zzz2400, zzz220000, ddb)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), bdd, bde, bdf) → new_pePe(new_lt13(zzz24000, zzz2200000, bdd), new_asAs(new_esEs24(zzz24000, zzz2200000, bdd), new_pePe(new_lt12(zzz24001, zzz2200001, bde), new_asAs(new_esEs25(zzz24001, zzz2200001, bde), new_ltEs11(zzz24002, zzz2200002, bdf)))))
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ea), eb)) → new_esEs7(zzz5001, zzz4001, ea, eb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, cda) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_esEs11(zzz5002, zzz4002, app(ty_[], ff)) → new_esEs18(zzz5002, zzz4002, ff)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(app(app(ty_@3, ceh), cfa), cfb)) → new_ltEs10(zzz24000, zzz2200000, ceh, cfa, cfb)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, cbb), cbc)) → new_lt4(zzz24000, zzz2200000, cbb, cbc)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, bf, bg) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, gd, ge, gf) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_lt6(zzz24000, zzz2200000, bh) → new_esEs8(new_compare0(zzz24000, zzz2200000, bh), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Maybe, ceg)) → new_ltEs17(zzz24000, zzz2200000, ceg)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_compare210(zzz24000, zzz2200000, True, bc) → EQ
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_lt9(zzz24001, zzz2200001, bfb)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, ccg) → new_fsEs(new_compare0(zzz2400, zzz220000, ccg))
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, cdh), cea), cda) → new_ltEs7(zzz24000, zzz2200000, cdh, cea)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_lt4(zzz24000, zzz2200000, bd, be) → new_esEs8(new_compare5(zzz24000, zzz2200000, bd, be), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, bd, be) → GT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), gh, ha) → new_asAs(new_esEs21(zzz5000, zzz4000, gh), new_esEs22(zzz5001, zzz4001, ha))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, cd), ce)) → new_esEs4(zzz5000, zzz4000, cd, ce)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_not(False) → True
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_compare12(zzz24000, zzz2200000, False, gd, ge, gf) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, app(ty_[], chf)) → new_esEs18(zzz5000, zzz4000, chf)
new_ltEs16(Left(zzz24000), Right(zzz2200000), cec, cda) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_ltEs19(zzz24001, zzz2200001, app(ty_[], cbe)) → new_ltEs12(zzz24001, zzz2200001, cbe)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, cda) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, df)) → new_esEs5(zzz5000, zzz4000, df)
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_lt17(zzz24000, zzz2200000, caf)
new_compare0(:(zzz24000, zzz24001), [], ccg) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, cff) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare26(zzz24000, zzz2200000, ddg, ddh, dea)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, bc)) → new_esEs5(zzz24000, zzz2200000, bc)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_lt9(zzz24000, zzz2200000, gg)
new_compare11(zzz235, zzz236, False, bf, bg) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, gc)) → new_esEs5(zzz5002, zzz4002, gc)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_lt18(zzz24001, zzz2200001, bee, bef, beg)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bfg), bfh), bga)) → new_ltEs10(zzz24002, zzz2200002, bfg, bfh, bga)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, bbh), bca)) → new_esEs4(zzz5000, zzz4000, bbh, bca)
new_ltEs17(Nothing, Just(zzz2200000), bge) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, cag), cah), cba)) → new_esEs6(zzz24000, zzz2200000, cag, cah, cba)
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bdg), bdh)) → new_esEs4(zzz24000, zzz2200000, bdg, bdh)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, dch), dda)) → new_ltEs7(zzz2400, zzz220000, dch, dda)
new_compare31(zzz24000, zzz2200000, bc) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, bc), bc)
new_ltEs17(Nothing, Nothing, bge) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_lt11(zzz24000, zzz2200000, cad, cae)
new_lt13(zzz24000, zzz2200000, app(ty_[], bh)) → new_lt6(zzz24000, zzz2200000, bh)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, beb), bec)) → new_lt11(zzz24001, zzz2200001, beb, bec)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, cbh)) → new_ltEs17(zzz24001, zzz2200001, cbh)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], cch), cda) → new_ltEs12(zzz24000, zzz2200000, cch)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_esEs16(True, True) → True
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, eh)) → new_esEs5(zzz5001, zzz4001, eh)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs6(zzz5000, zzz4000, dbb, dbc, dbd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, bd), be)) → new_lt4(zzz24000, zzz2200000, bd, be)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], cac)) → new_esEs18(zzz24000, zzz2200000, cac)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, gd, ge, gf) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, gd, ge, gf), gd, ge, gf)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ccd), cce)) → new_ltEs7(zzz24001, zzz2200001, ccd, cce)
new_asAs(False, zzz230) → False
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zzz5001, zzz4001, ed, ee, ef)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, ddf)) → new_compare31(zzz24000, zzz2200000, ddf)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, fa), fb)) → new_esEs4(zzz5002, zzz4002, fa, fb)
new_esEs18([], [], bbg) → True
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs6(zzz5000, zzz4000, bce, bcf, bcg)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, ddd), dde)) → new_compare19(zzz24000, zzz2200000, ddd, dde)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, bcb), bcc)) → new_esEs7(zzz5000, zzz4000, bcb, bcc)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, cgh), cff) → new_esEs5(zzz5000, zzz4000, cgh)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, cad), cae)) → new_esEs4(zzz24000, zzz2200000, cad, cae)
new_compare211(Right(zzz2400), Left(zzz220000), False, bdb, bdc) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, bda)) → new_esEs5(zzz5000, zzz4000, bda)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, bee), bef), beg)) → new_esEs6(zzz24001, zzz2200001, bee, bef, beg)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cgc), cff) → new_esEs18(zzz5000, zzz4000, cgc)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, bdb, bdc) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, bgb), bgc)) → new_ltEs7(zzz24002, zzz2200002, bgb, bgc)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), dad) → False
new_esEs5(Just(zzz5000), Nothing, dad) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Left(zzz2200000), cec, cda) → False
new_compare211(zzz240, zzz22000, True, bdb, bdc) → EQ
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cga), cgb), cff) → new_esEs7(zzz5000, zzz4000, cga, cgb)
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, cbd)) → new_esEs20(zzz24000, zzz2200000, cbd)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, app(ty_Ratio, cfe)) → new_ltEs5(zzz24000, zzz2200000, cfe)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), cec, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, cda) → new_ltEs13(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, bhe), bhf)) → new_ltEs7(zzz24000, zzz2200000, bhe, bhf)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, dad) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, caf)) → new_esEs5(zzz24000, zzz2200000, caf)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), cha, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bfd), bfe)) → new_ltEs16(zzz24002, zzz2200002, bfd, bfe)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, de)) → new_esEs20(zzz5000, zzz4000, de)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs10(zzz2400, zzz220000, dce, dcf, dcg)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, bd, be) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, bd, be), bd, be)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, bha)) → new_ltEs17(zzz24000, zzz2200000, bha)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, bbe)) → new_esEs5(zzz5001, zzz4001, bbe)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bac)) → new_esEs5(zzz5000, zzz4000, bac)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zzz5000, zzz4000, db, dc, dd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_compare0([], :(zzz2200000, zzz2200001), ccg) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, hg), hh), baa)) → new_esEs6(zzz5000, zzz4000, hg, hh, baa)
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_asAs(True, zzz230) → zzz230
new_esEs4(Right(zzz5000), Left(zzz4000), cha, cff) → False
new_esEs4(Left(zzz5000), Right(zzz4000), cha, cff) → False
new_lt11(zzz240, zzz22000, bdb, bdc) → new_esEs8(new_compare19(zzz240, zzz22000, bdb, bdc), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dag), dah)) → new_esEs7(zzz5000, zzz4000, dag, dah)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cgd), cge), cgf), cff) → new_esEs6(zzz5000, zzz4000, cgd, cge, cgf)
new_lt12(zzz24001, zzz2200001, app(ty_[], bea)) → new_lt6(zzz24001, zzz2200001, bea)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_compare19(zzz240, zzz22000, bdb, bdc) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, bdb, bdc), bdb, bdc)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, cdb), cdc), cda) → new_ltEs16(zzz24000, zzz2200000, cdb, cdc)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, gg)) → new_esEs20(zzz24000, zzz2200000, gg)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs10(zzz2400, zzz220000, bdd, bde, bdf)
new_ltEs5(zzz2400, zzz220000, bbf) → new_fsEs(new_compare9(zzz2400, zzz220000, bbf))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, gd), ge), gf)) → new_lt18(zzz24000, zzz2200000, gd, ge, gf)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, cca), ccb), ccc)) → new_ltEs10(zzz24001, zzz2200001, cca, ccb, ccc)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), ca, cb, cc) → new_asAs(new_esEs9(zzz5000, zzz4000, ca), new_asAs(new_esEs10(zzz5001, zzz4001, cb), new_esEs11(zzz5002, zzz4002, cc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, cff) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bff)) → new_ltEs17(zzz24002, zzz2200002, bff)
new_esEs23(zzz5000, zzz4000, app(ty_[], bcd)) → new_esEs18(zzz5000, zzz4000, bcd)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, ceb), cda) → new_ltEs5(zzz24000, zzz2200000, ceb)
new_primCompAux00(zzz266, GT) → GT
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, cbf), cbg)) → new_ltEs16(zzz24001, zzz2200001, cbf, cbg)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dba)) → new_esEs18(zzz5000, zzz4000, dba)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, dcb), dcc)) → new_ltEs16(zzz2400, zzz220000, dcb, dcc)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dae), daf)) → new_esEs4(zzz5000, zzz4000, dae, daf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, cde), cdf), cdg), cda) → new_ltEs10(zzz24000, zzz2200000, cde, cdf, cdg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bfb)) → new_esEs20(zzz24001, zzz2200001, bfb)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_sr(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(x0, x1, True)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, x2)
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(EQ, EQ)
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_compare30(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs15(x0, x1)
new_esEs10(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(True, False)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(False, True)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs9(x0, x1, ty_Float)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_ltEs18(x0, x1)
new_esEs10(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_compare211(x0, x1, True, x2, x3)
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs16(True, False)
new_esEs16(False, True)
new_esEs18([], :(x0, x1), x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Nothing, Nothing, x0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Float)
new_ltEs12(x0, x1, x2)
new_esEs25(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs28(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_compare28(x0, x1, True)
new_compare210(x0, x1, False, x2)
new_primEqNat0(Zero, Zero)
new_compare0(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs18([], [], x0)
new_compare32(x0, x1, ty_Integer)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs15(Char(x0), Char(x1))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt15(x0, x1)
new_fsEs(x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Int)
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs17(Nothing, Just(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, False)
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare25(x0, x1, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs21(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_esEs9(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare0([], [], x0)
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2)
new_lt7(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Integer)
new_lt12(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Float)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2)
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_ltEs17(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, ty_@0)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs11(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1)
new_ltEs13(x0, x1)
new_esEs11(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Integer)
new_lt9(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, x2, x3)
new_compare6(@0, @0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(GT, GT)
new_lt20(x0, x1, ty_Char)
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_lt12(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare24(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(False, False)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt13(x0, x1, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs14(True, True)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(False, False)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1)
new_compare27(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Float)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare5(x0, x1, x2, x3)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs11(x0, x1, ty_Char)
new_compare17(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_Bool)
new_compare11(x0, x1, True, x2, x3)
new_gt1(x0, x1, x2, x3)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, True, x2, x3)
new_lt11(x0, x1, x2, x3)
new_ltEs11(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Just(x0), x1)
new_lt18(x0, x1, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Char)
new_compare110(x0, x1, False, x2, x3)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_lt12(x0, x1, ty_Bool)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare13(x0, x1, False)
new_ltEs21(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)

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
                                  ↳ QDP
                                  ↳ 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_intersectFM_C2IntersectFM_C15(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, zzz343, zzz344, False, cc, cd, ce, cf, cg, da) → new_intersectFM_C(zzz335, new_intersectFM_C2Gts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg), zzz339, cc, cd, ce, cf, cg)
new_intersectFM_C2IntersectFM_C11(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, EmptyFM, h, ba, bb, bc, bd, be) → new_intersectFM_C(zzz318, new_intersectFM_C2Lts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd), zzz321, h, ba, bb, bc, bd)
new_intersectFM_C2IntersectFM_C13(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, EmptyFM, zzz363, True, db, dc, dd, de, df, dg) → new_intersectFM_C(zzz354, new_intersectFM_C2Lts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df), zzz357, db, dc, dd, de, df)
new_intersectFM_C2IntersectFM_C1(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, Branch(zzz3260, zzz3261, zzz3262, zzz3263, zzz3264), zzz327, True, h, ba, bb, bc, bd, be) → new_intersectFM_C2IntersectFM_C1(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz3260, zzz3261, zzz3262, zzz3263, zzz3264, new_lt11(Left(zzz317), zzz3260, h, ba), h, ba, bb, bc, bd, be)
new_intersectFM_C2IntersectFM_C13(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, zzz362, zzz363, False, db, dc, dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, zzz362, zzz363, new_gt0(zzz353, zzz359, db, dc), db, dc, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C12(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, EmptyFM, zzz344, True, cc, cd, ce, cf, cg, da) → new_intersectFM_C(zzz335, new_intersectFM_C2Gts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg), zzz339, cc, cd, ce, cf, cg)
new_intersectFM_C(zzz3, Branch(Left(zzz400), zzz41, zzz42, zzz43, zzz44), Branch(Right(zzz500), zzz51, zzz52, zzz53, zzz54), bf, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C13(zzz400, zzz41, zzz42, zzz43, zzz44, zzz500, zzz3, zzz51, zzz52, zzz53, zzz54, Left(zzz400), zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare211(Right(zzz500), Left(zzz400), False, bf, bg), LT), bf, bg, bh, ca, cb, cb)
new_intersectFM_C2IntersectFM_C15(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, zzz343, zzz344, True, cc, cd, ce, cf, cg, da) → new_intersectFM_C2IntersectFM_C16(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz344, cc, cd, ce, cf, cg, da)
new_intersectFM_C2IntersectFM_C10(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, zzz326, zzz327, False, h, ba, bb, bc, bd, be) → new_intersectFM_C(zzz318, new_intersectFM_C2Gts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd), zzz322, h, ba, bb, bc, bd)
new_intersectFM_C2IntersectFM_C19(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, zzz379, zzz380, False, dh, ea, eb, ec, ed, ee) → new_intersectFM_C(zzz371, new_intersectFM_C2Gts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed), zzz375, dh, ea, eb, ec, ed)
new_intersectFM_C2IntersectFM_C16(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, EmptyFM, cc, cd, ce, cf, cg, da) → new_intersectFM_C(zzz335, new_intersectFM_C2Gts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg), zzz339, cc, cd, ce, cf, cg)
new_intersectFM_C2IntersectFM_C110(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, Branch(zzz3790, zzz3791, zzz3792, zzz3793, zzz3794), dh, ea, eb, ec, ed, ee) → new_intersectFM_C2IntersectFM_C14(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz3790, zzz3791, zzz3792, zzz3793, zzz3794, new_lt11(Right(zzz370), zzz3790, dh, ea), dh, ea, eb, ec, ed, ee)
new_intersectFM_C2IntersectFM_C19(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, zzz379, zzz380, True, dh, ea, eb, ec, ed, ee) → new_intersectFM_C2IntersectFM_C110(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz380, dh, ea, eb, ec, ed, ee)
new_intersectFM_C2IntersectFM_C13(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, EmptyFM, zzz363, True, db, dc, dd, de, df, dg) → new_intersectFM_C(zzz354, new_intersectFM_C2Gts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df), zzz358, db, dc, dd, de, df)
new_intersectFM_C2IntersectFM_C19(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, zzz379, zzz380, False, dh, ea, eb, ec, ed, ee) → new_intersectFM_C(zzz371, new_intersectFM_C2Lts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed), zzz374, dh, ea, eb, ec, ed)
new_intersectFM_C2IntersectFM_C18(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, Branch(zzz3620, zzz3621, zzz3622, zzz3623, zzz3624), db, dc, dd, de, df, dg) → new_intersectFM_C2IntersectFM_C13(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz3620, zzz3621, zzz3622, zzz3623, zzz3624, new_lt11(Right(zzz353), zzz3620, db, dc), db, dc, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C18(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, EmptyFM, db, dc, dd, de, df, dg) → new_intersectFM_C(zzz354, new_intersectFM_C2Lts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df), zzz357, db, dc, dd, de, df)
new_intersectFM_C2IntersectFM_C11(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, EmptyFM, h, ba, bb, bc, bd, be) → new_intersectFM_C(zzz318, new_intersectFM_C2Gts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd), zzz322, h, ba, bb, bc, bd)
new_intersectFM_C2IntersectFM_C11(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, Branch(zzz3260, zzz3261, zzz3262, zzz3263, zzz3264), h, ba, bb, bc, bd, be) → new_intersectFM_C2IntersectFM_C1(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz3260, zzz3261, zzz3262, zzz3263, zzz3264, new_lt11(Left(zzz317), zzz3260, h, ba), h, ba, bb, bc, bd, be)
new_intersectFM_C2IntersectFM_C12(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, Branch(zzz3430, zzz3431, zzz3432, zzz3433, zzz3434), zzz344, True, cc, cd, ce, cf, cg, da) → new_intersectFM_C2IntersectFM_C12(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz3430, zzz3431, zzz3432, zzz3433, zzz3434, new_lt11(Left(zzz334), zzz3430, cc, cd), cc, cd, ce, cf, cg, da)
new_intersectFM_C2IntersectFM_C16(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, EmptyFM, cc, cd, ce, cf, cg, da) → new_intersectFM_C(zzz335, new_intersectFM_C2Lts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg), zzz338, cc, cd, ce, cf, cg)
new_intersectFM_C2IntersectFM_C17(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, zzz362, zzz363, False, db, dc, dd, de, df, dg) → new_intersectFM_C(zzz354, new_intersectFM_C2Lts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df), zzz357, db, dc, dd, de, df)
new_intersectFM_C2IntersectFM_C16(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, Branch(zzz3430, zzz3431, zzz3432, zzz3433, zzz3434), cc, cd, ce, cf, cg, da) → new_intersectFM_C2IntersectFM_C12(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz3430, zzz3431, zzz3432, zzz3433, zzz3434, new_lt11(Left(zzz334), zzz3430, cc, cd), cc, cd, ce, cf, cg, da)
new_intersectFM_C2IntersectFM_C1(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, EmptyFM, zzz327, True, h, ba, bb, bc, bd, be) → new_intersectFM_C(zzz318, new_intersectFM_C2Lts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd), zzz321, h, ba, bb, bc, bd)
new_intersectFM_C(zzz3, Branch(Right(zzz400), zzz41, zzz42, zzz43, zzz44), Branch(Left(zzz500), zzz51, zzz52, zzz53, zzz54), bf, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C12(zzz400, zzz41, zzz42, zzz43, zzz44, zzz500, zzz3, zzz51, zzz52, zzz53, zzz54, Right(zzz400), zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare211(Left(zzz500), Right(zzz400), False, bf, bg), LT), bf, bg, bh, ca, cb, cb)
new_intersectFM_C2IntersectFM_C1(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, EmptyFM, zzz327, True, h, ba, bb, bc, bd, be) → new_intersectFM_C(zzz318, new_intersectFM_C2Gts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd), zzz322, h, ba, bb, bc, bd)
new_intersectFM_C2IntersectFM_C13(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, Branch(zzz3620, zzz3621, zzz3622, zzz3623, zzz3624), zzz363, True, db, dc, dd, de, df, dg) → new_intersectFM_C2IntersectFM_C13(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz3620, zzz3621, zzz3622, zzz3623, zzz3624, new_lt11(Right(zzz353), zzz3620, db, dc), db, dc, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C14(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, EmptyFM, zzz380, True, dh, ea, eb, ec, ed, ee) → new_intersectFM_C(zzz371, new_intersectFM_C2Lts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed), zzz374, dh, ea, eb, ec, ed)
new_intersectFM_C2IntersectFM_C17(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, zzz362, zzz363, False, db, dc, dd, de, df, dg) → new_intersectFM_C(zzz354, new_intersectFM_C2Gts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df), zzz358, db, dc, dd, de, df)
new_intersectFM_C2IntersectFM_C17(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz359, zzz360, zzz361, zzz362, zzz363, True, db, dc, dd, de, df, dg) → new_intersectFM_C2IntersectFM_C18(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, zzz363, db, dc, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C110(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, EmptyFM, dh, ea, eb, ec, ed, ee) → new_intersectFM_C(zzz371, new_intersectFM_C2Gts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed), zzz375, dh, ea, eb, ec, ed)
new_intersectFM_C2IntersectFM_C12(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, EmptyFM, zzz344, True, cc, cd, ce, cf, cg, da) → new_intersectFM_C(zzz335, new_intersectFM_C2Lts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg), zzz338, cc, cd, ce, cf, cg)
new_intersectFM_C2IntersectFM_C10(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, zzz326, zzz327, True, h, ba, bb, bc, bd, be) → new_intersectFM_C2IntersectFM_C11(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz327, h, ba, bb, bc, bd, be)
new_intersectFM_C2IntersectFM_C10(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, zzz326, zzz327, False, h, ba, bb, bc, bd, be) → new_intersectFM_C(zzz318, new_intersectFM_C2Lts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd), zzz321, h, ba, bb, bc, bd)
new_intersectFM_C(zzz3, Branch(Left(zzz400), zzz41, zzz42, zzz43, zzz44), Branch(Left(zzz500), zzz51, zzz52, zzz53, zzz54), bf, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C1(zzz400, zzz41, zzz42, zzz43, zzz44, zzz500, zzz3, zzz51, zzz52, zzz53, zzz54, Left(zzz400), zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare211(Left(zzz500), Left(zzz400), new_esEs29(zzz500, zzz400, bf), bf, bg), LT), bf, bg, bh, ca, cb, cb)
new_intersectFM_C2IntersectFM_C14(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, Branch(zzz3790, zzz3791, zzz3792, zzz3793, zzz3794), zzz380, True, dh, ea, eb, ec, ed, ee) → new_intersectFM_C2IntersectFM_C14(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz3790, zzz3791, zzz3792, zzz3793, zzz3794, new_lt11(Right(zzz370), zzz3790, dh, ea), dh, ea, eb, ec, ed, ee)
new_intersectFM_C2IntersectFM_C15(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, zzz343, zzz344, False, cc, cd, ce, cf, cg, da) → new_intersectFM_C(zzz335, new_intersectFM_C2Lts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg), zzz338, cc, cd, ce, cf, cg)
new_intersectFM_C2IntersectFM_C110(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, EmptyFM, dh, ea, eb, ec, ed, ee) → new_intersectFM_C(zzz371, new_intersectFM_C2Lts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed), zzz374, dh, ea, eb, ec, ed)
new_intersectFM_C2IntersectFM_C1(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, zzz326, zzz327, False, h, ba, bb, bc, bd, be) → new_intersectFM_C2IntersectFM_C10(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, zzz318, zzz319, zzz320, zzz321, zzz322, zzz323, zzz324, zzz325, zzz326, zzz327, new_gt1(zzz317, zzz323, h, ba), h, ba, bb, bc, bd, be)
new_intersectFM_C(zzz3, Branch(Right(zzz400), zzz41, zzz42, zzz43, zzz44), Branch(Right(zzz500), zzz51, zzz52, zzz53, zzz54), bf, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C14(zzz400, zzz41, zzz42, zzz43, zzz44, zzz500, zzz3, zzz51, zzz52, zzz53, zzz54, Right(zzz400), zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare211(Right(zzz500), Right(zzz400), new_esEs30(zzz500, zzz400, bg), bf, bg), LT), bf, bg, bh, ca, cb, cb)
new_intersectFM_C2IntersectFM_C14(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, EmptyFM, zzz380, True, dh, ea, eb, ec, ed, ee) → new_intersectFM_C(zzz371, new_intersectFM_C2Gts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed), zzz375, dh, ea, eb, ec, ed)
new_intersectFM_C2IntersectFM_C12(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, zzz343, zzz344, False, cc, cd, ce, cf, cg, da) → new_intersectFM_C2IntersectFM_C15(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, zzz335, zzz336, zzz337, zzz338, zzz339, zzz340, zzz341, zzz342, zzz343, zzz344, new_gt1(zzz334, zzz340, cc, cd), cc, cd, ce, cf, cg, da)
new_intersectFM_C2IntersectFM_C18(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, zzz354, zzz355, zzz356, zzz357, zzz358, EmptyFM, db, dc, dd, de, df, dg) → new_intersectFM_C(zzz354, new_intersectFM_C2Gts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df), zzz358, db, dc, dd, de, df)
new_intersectFM_C2IntersectFM_C14(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, zzz379, zzz380, False, dh, ea, eb, ec, ed, ee) → new_intersectFM_C2IntersectFM_C19(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, zzz371, zzz372, zzz373, zzz374, zzz375, zzz376, zzz377, zzz378, zzz379, zzz380, new_gt0(zzz370, zzz376, dh, ea), dh, ea, eb, ec, ed, ee)

The TRS R consists of the following rules:

new_esEs29(zzz500, zzz400, ty_Integer) → new_esEs17(zzz500, zzz400)
new_esEs28(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_ltEs4(zzz2400, zzz220000) → new_fsEs(new_compare6(zzz2400, zzz220000))
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Int) → new_esEs19(zzz24001, zzz2200001)
new_compare211(Right(zzz2400), Right(zzz220000), False, cgb, cgc) → new_compare110(zzz2400, zzz220000, new_ltEs21(zzz2400, zzz220000, cgc), cgb, cgc)
new_ltEs20(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_ltEs21(zzz2400, zzz220000, app(ty_[], eaa)) → new_ltEs12(zzz2400, zzz220000, eaa)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs24(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare110(zzz242, zzz243, True, dhg, dhh) → LT
new_lt18(zzz24000, zzz2200000, bfe, bff, bfg) → new_esEs8(new_compare26(zzz24000, zzz2200000, bfe, bff, bfg), LT)
new_esEs28(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs6(zzz5000, zzz4000, cce, ccf, ccg)
new_compare32(zzz24000, zzz2200000, app(app(ty_@2, ceb), cec)) → new_compare5(zzz24000, zzz2200000, ceb, cec)
new_compare211(Left(zzz2400), Left(zzz220000), False, cgb, cgc) → new_compare11(zzz2400, zzz220000, new_ltEs20(zzz2400, zzz220000, cgb), cgb, cgc)
new_esEs9(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, app(ty_Maybe, cda)) → new_esEs5(zzz5000, zzz4000, cda)
new_ltEs11(zzz24002, zzz2200002, app(ty_Ratio, cac)) → new_ltEs5(zzz24002, zzz2200002, cac)
new_ltEs19(zzz24001, zzz2200001, app(ty_Ratio, ddf)) → new_ltEs5(zzz24001, zzz2200001, ddf)
new_compare32(zzz24000, zzz2200000, ty_Double) → new_compare7(zzz24000, zzz2200000)
new_esEs29(zzz500, zzz400, app(ty_Ratio, bef)) → new_esEs20(zzz500, zzz400, bef)
new_ltEs20(zzz2400, zzz220000, app(app(ty_Either, dfb), ddh)) → new_ltEs16(zzz2400, zzz220000, dfb, ddh)
new_esEs11(zzz5002, zzz4002, app(app(ty_@2, bac), bad)) → new_esEs7(zzz5002, zzz4002, bac, bad)
new_primMulNat0(Zero, Zero) → Zero
new_compare27(zzz24000, zzz2200000) → new_compare28(zzz24000, zzz2200000, new_esEs16(zzz24000, zzz2200000))
new_lt12(zzz24001, zzz2200001, app(app(ty_@2, bgg), bgh)) → new_lt4(zzz24001, zzz2200001, bgg, bgh)
new_splitLT21(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, False, h, ba, bd) → new_splitLT11(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, new_gt1(zzz317, zzz3150, h, ba), h, ba, bd)
new_primCompAux0(zzz24000, zzz2200000, zzz257, cdb) → new_primCompAux00(zzz257, new_compare32(zzz24000, zzz2200000, cdb))
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_[], cge)) → new_ltEs12(zzz24000, zzz2200000, cge)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_lt13(zzz24000, zzz2200000, app(ty_Maybe, ef)) → new_lt17(zzz24000, zzz2200000, ef)
new_esEs11(zzz5002, zzz4002, ty_Char) → new_esEs15(zzz5002, zzz4002)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Float, ddh) → new_ltEs18(zzz24000, zzz2200000)
new_lt14(zzz24000, zzz2200000) → new_esEs8(new_compare27(zzz24000, zzz2200000), LT)
new_lt20(zzz24000, zzz2200000, app(app(app(ty_@3, dbg), dbh), dca)) → new_lt18(zzz24000, zzz2200000, dbg, dbh, dca)
new_lt20(zzz24000, zzz2200000, app(ty_[], dbc)) → new_lt6(zzz24000, zzz2200000, dbc)
new_ltEs14(False, True) → True
new_esEs29(zzz500, zzz400, app(app(ty_Either, bec), bed)) → new_esEs4(zzz500, zzz400, bec, bed)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Ratio, dhe)) → new_esEs20(zzz5000, zzz4000, dhe)
new_esEs18(:(zzz5000, zzz5001), :(zzz4000, zzz4001), bee) → new_asAs(new_esEs23(zzz5000, zzz4000, bee), new_esEs18(zzz5001, zzz4001, bee))
new_compare32(zzz24000, zzz2200000, ty_Ordering) → new_compare30(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Ratio, chf)) → new_ltEs5(zzz24000, zzz2200000, chf)
new_esEs23(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_splitGT12(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, True, db, dc, df) → new_mkVBalBranch0(zzz3520, zzz3521, new_splitGT4(zzz3523, zzz353, db, dc, df), zzz3524, db, dc, df)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bed) → new_esEs14(zzz5000, zzz4000)
new_compare7(Double(zzz24000, zzz24001), Double(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_splitGT22(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, True, db, dc, df) → new_splitGT4(zzz3524, zzz353, db, dc, df)
new_mkBalBranch6Size_r(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb) → new_sizeFM0(zzz3934, h, ba, bb)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Bool, ddh) → new_ltEs14(zzz24000, zzz2200000)
new_splitLT11(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, False, h, ba, bd) → zzz3153
new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df) → new_sizeFM(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df)
new_lt13(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_lt9(zzz24000, zzz2200000, bbd) → new_esEs8(new_compare9(zzz24000, zzz2200000, bbd), LT)
new_compare28(zzz24000, zzz2200000, False) → new_compare16(zzz24000, zzz2200000, new_ltEs14(zzz24000, zzz2200000))
new_mkBalBranch6MkBalBranch01(zzz3930, zzz3931, zzz432, zzz39340, zzz39341, zzz39342, Branch(zzz393430, zzz393431, zzz393432, zzz393433, zzz393434), zzz39344, False, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz393430, zzz393431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz3930, zzz3931, zzz432, zzz393433, app(app(ty_Either, h), ba), bb), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz39340, zzz39341, zzz393434, zzz39344, app(app(ty_Either, h), ba), bb), app(app(ty_Either, h), ba), bb)
new_compare0(:(zzz24000, zzz24001), :(zzz2200000, zzz2200001), cdb) → new_primCompAux0(zzz24000, zzz2200000, new_compare0(zzz24001, zzz2200001, cdb), cdb)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Int) → new_ltEs9(zzz24002, zzz2200002)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dhf)) → new_esEs5(zzz5000, zzz4000, dhf)
new_ltEs8(EQ, EQ) → True
new_lt20(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs25(zzz24001, zzz2200001, ty_Integer) → new_esEs17(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, app(ty_[], bhb)) → new_ltEs12(zzz24002, zzz2200002, bhb)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(app(ty_@3, cha), chb), chc)) → new_ltEs10(zzz24000, zzz2200000, cha, chb, chc)
new_esEs12(@0, @0) → True
new_mkVBalBranch0(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), EmptyFM, db, dc, df) → new_addToFM(Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz3510, zzz3511, db, dc, df)
new_esEs28(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_@0) → new_lt5(zzz24000, zzz2200000)
new_esEs11(zzz5002, zzz4002, app(ty_Ratio, bba)) → new_esEs20(zzz5002, zzz4002, bba)
new_esEs30(zzz500, zzz400, ty_Double) → new_esEs13(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, app(ty_[], dfc)) → new_ltEs12(zzz24000, zzz2200000, dfc)
new_compare32(zzz24000, zzz2200000, app(ty_Ratio, ced)) → new_compare9(zzz24000, zzz2200000, ced)
new_ltEs7(@2(zzz24000, zzz24001), @2(zzz2200000, zzz2200001), dba, dbb) → new_pePe(new_lt20(zzz24000, zzz2200000, dba), new_asAs(new_esEs28(zzz24000, zzz2200000, dba), new_ltEs19(zzz24001, zzz2200001, dbb)))
new_esEs17(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, ty_Char) → new_ltEs13(zzz24002, zzz2200002)
new_compare24(zzz24000, zzz2200000, False, eg, eh) → new_compare17(zzz24000, zzz2200000, new_ltEs7(zzz24000, zzz2200000, eg, eh), eg, eh)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bed) → new_esEs8(zzz5000, zzz4000)
new_lt20(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs15(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_splitLT4(EmptyFM, zzz353, db, dc, df) → new_emptyFM(db, dc, df)
new_esEs9(zzz5000, zzz4000, app(ty_[], ga)) → new_esEs18(zzz5000, zzz4000, ga)
new_esEs10(zzz5001, zzz4001, app(ty_Ratio, hg)) → new_esEs20(zzz5001, zzz4001, hg)
new_lt20(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_pePe(False, zzz256) → zzz256
new_primPlusInt0(zzz43220, Pos(zzz5550)) → Pos(new_primPlusNat0(zzz43220, zzz5550))
new_esEs25(zzz24001, zzz2200001, app(app(ty_@2, bgg), bgh)) → new_esEs7(zzz24001, zzz2200001, bgg, bgh)
new_gt2(zzz551, zzz550) → new_esEs8(new_compare18(zzz551, zzz550), GT)
new_esEs25(zzz24001, zzz2200001, app(app(ty_Either, bga), bgb)) → new_esEs4(zzz24001, zzz2200001, bga, bgb)
new_esEs18([], :(zzz4000, zzz4001), bee) → False
new_esEs18(:(zzz5000, zzz5001), [], bee) → False
new_compare6(@0, @0) → EQ
new_esEs23(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_esEs22(zzz5001, zzz4001, app(app(ty_Either, bda), bdb)) → new_esEs4(zzz5001, zzz4001, bda, bdb)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Nothing, cgd) → False
new_compare15(Char(zzz24000), Char(zzz2200000)) → new_primCmpNat0(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Float) → new_esEs14(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, app(ty_Maybe, cgd)) → new_ltEs17(zzz2400, zzz220000, cgd)
new_gt0(zzz353, zzz359, db, dc) → new_esEs8(new_compare19(Right(zzz353), zzz359, db, dc), GT)
new_ltEs19(zzz24001, zzz2200001, ty_Integer) → new_ltEs6(zzz24001, zzz2200001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_ltEs11(zzz24002, zzz2200002, ty_Ordering) → new_ltEs8(zzz24002, zzz2200002)
new_esEs9(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs20(zzz2400, zzz220000, ty_Ordering) → new_ltEs8(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, ty_Bool) → new_compare27(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Int) → new_ltEs9(zzz2400, zzz220000)
new_esEs22(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs8(EQ, GT) → True
new_ltEs8(GT, GT) → True
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Succ(zzz220000))) → new_primCmpNat0(zzz220000, zzz2400)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Maybe, dec), ddh) → new_ltEs17(zzz24000, zzz2200000, dec)
new_compare10(zzz24000, zzz2200000, True, ef) → LT
new_mkBalBranch6MkBalBranch01(zzz3930, zzz3931, zzz432, zzz39340, zzz39341, zzz39342, zzz39343, zzz39344, True, h, ba, bb) → new_mkBranch(Succ(Succ(Zero)), zzz39340, zzz39341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz3930, zzz3931, zzz432, zzz39343, app(app(ty_Either, h), ba), bb), zzz39344, app(app(ty_Either, h), ba), bb)
new_primPlusInt1(zzz43220, Pos(zzz5560)) → new_primMinusNat0(zzz5560, zzz43220)
new_ltEs20(zzz2400, zzz220000, app(ty_[], cdb)) → new_ltEs12(zzz2400, zzz220000, cdb)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primCmpNat0(Zero, Succ(zzz22000000)) → LT
new_ltEs20(zzz2400, zzz220000, app(app(ty_@2, dba), dbb)) → new_ltEs7(zzz2400, zzz220000, dba, dbb)
new_mkBranch(zzz667, zzz668, zzz669, zzz670, zzz671, cad, cae) → Branch(zzz668, zzz669, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM1(zzz670, cad, cae)), zzz670, zzz671, zzz668, cad, cae), zzz670, zzz671)
new_compare18(zzz24, zzz2200) → new_primCmpInt(zzz24, zzz2200)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, app(app(ty_@2, ccb), ccc)) → new_esEs7(zzz5000, zzz4000, ccb, ccc)
new_esEs25(zzz24001, zzz2200001, ty_Bool) → new_esEs16(zzz24001, zzz2200001)
new_ltEs20(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_esEs25(zzz24001, zzz2200001, ty_@0) → new_esEs12(zzz24001, zzz2200001)
new_esEs8(LT, LT) → True
new_ltEs20(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_esEs11(zzz5002, zzz4002, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5002, zzz4002, baf, bag, bah)
new_lt13(zzz24000, zzz2200000, ty_Integer) → new_lt16(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs8(LT, EQ) → True
new_lt20(zzz24000, zzz2200000, app(ty_Ratio, dcd)) → new_lt9(zzz24000, zzz2200000, dcd)
new_addToFM_C20(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, False, db, dc, df) → new_addToFM_C10(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, new_gt(zzz3510, zzz4870, db, dc), db, dc, df)
new_lt12(zzz24001, zzz2200001, ty_Bool) → new_lt14(zzz24001, zzz2200001)
new_esEs29(zzz500, zzz400, app(app(ty_@2, bbe), bbf)) → new_esEs7(zzz500, zzz400, bbe, bbf)
new_esEs25(zzz24001, zzz2200001, ty_Ordering) → new_esEs8(zzz24001, zzz2200001)
new_lt10(zzz24000, zzz2200000) → new_esEs8(new_compare15(zzz24000, zzz2200000), LT)
new_intersectFM_C2Lts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd) → new_splitLT21(Left(zzz312), zzz313, zzz314, zzz315, zzz316, zzz317, new_lt11(Left(zzz317), Left(zzz312), h, ba), h, ba, bd)
new_compare10(zzz24000, zzz2200000, False, ef) → GT
new_esEs10(zzz5001, zzz4001, app(app(ty_Either, gg), gh)) → new_esEs4(zzz5001, zzz4001, gg, gh)
new_intersectFM_C2Gts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df) → new_splitGT22(Left(zzz348), zzz349, zzz350, zzz351, zzz352, zzz353, new_gt0(zzz353, Left(zzz348), db, dc), db, dc, df)
new_esEs30(zzz500, zzz400, ty_@0) → new_esEs12(zzz500, zzz400)
new_mkVBalBranch3MkVBalBranch10(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, db, dc, df) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), app(app(ty_Either, db), dc), df)
new_lt13(zzz24000, zzz2200000, ty_Bool) → new_lt14(zzz24000, zzz2200000)
new_pePe(True, zzz256) → True
new_compare0([], [], cdb) → EQ
new_primEqNat0(Zero, Zero) → True
new_lt12(zzz24001, zzz2200001, ty_@0) → new_lt5(zzz24001, zzz2200001)
new_ltEs11(zzz24002, zzz2200002, ty_@0) → new_ltEs4(zzz24002, zzz2200002)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, app(app(ty_@2, dgb), dgc)) → new_ltEs7(zzz24000, zzz2200000, dgb, dgc)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat1(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_esEs25(zzz24001, zzz2200001, app(ty_[], bfh)) → new_esEs18(zzz24001, zzz2200001, bfh)
new_ltEs21(zzz2400, zzz220000, app(ty_Maybe, ead)) → new_ltEs17(zzz2400, zzz220000, ead)
new_addToFM(zzz487, zzz3510, zzz3511, db, dc, df) → new_addToFM_C0(zzz487, zzz3510, zzz3511, db, dc, df)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs30(zzz500, zzz400, app(ty_Ratio, dag)) → new_esEs20(zzz500, zzz400, dag)
new_esEs24(zzz24000, zzz2200000, app(ty_[], bbc)) → new_esEs18(zzz24000, zzz2200000, bbc)
new_esEs22(zzz5001, zzz4001, app(app(ty_@2, bdc), bdd)) → new_esEs7(zzz5001, zzz4001, bdc, bdd)
new_ltEs8(GT, EQ) → False
new_lt17(zzz24000, zzz2200000, ef) → new_esEs8(new_compare31(zzz24000, zzz2200000, ef), LT)
new_ltEs8(EQ, LT) → False
new_lt13(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_compare110(zzz242, zzz243, False, dhg, dhh) → GT
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Integer) → new_compare14(new_sr0(zzz24000, zzz2200001), new_sr0(zzz2200000, zzz24001))
new_ltEs21(zzz2400, zzz220000, ty_@0) → new_ltEs4(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_Either, cgf), cgg)) → new_ltEs16(zzz24000, zzz2200000, cgf, cgg)
new_esEs15(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_sr(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare12(zzz24000, zzz2200000, True, bfe, bff, bfg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cbf), bed) → new_esEs20(zzz5000, zzz4000, cbf)
new_esEs11(zzz5002, zzz4002, ty_Double) → new_esEs13(zzz5002, zzz4002)
new_esEs24(zzz24000, zzz2200000, app(app(ty_@2, eg), eh)) → new_esEs7(zzz24000, zzz2200000, eg, eh)
new_splitGT21(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, True, h, ba, bd) → new_splitGT3(zzz3164, zzz317, h, ba, bd)
new_compare32(zzz24000, zzz2200000, ty_@0) → new_compare6(zzz24000, zzz2200000)
new_esEs8(GT, GT) → True
new_esEs11(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs10(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_esEs30(zzz500, zzz400, ty_Int) → new_esEs19(zzz500, zzz400)
new_esEs22(zzz5001, zzz4001, app(ty_[], bde)) → new_esEs18(zzz5001, zzz4001, bde)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_addToFM_C0(EmptyFM, zzz3510, zzz3511, db, dc, df) → Branch(zzz3510, zzz3511, Pos(Succ(Zero)), new_emptyFM(db, dc, df), new_emptyFM(db, dc, df))
new_compare210(zzz24000, zzz2200000, False, ef) → new_compare10(zzz24000, zzz2200000, new_ltEs17(zzz24000, zzz2200000, ef), ef)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_@0, ddh) → new_ltEs4(zzz24000, zzz2200000)
new_compare17(zzz24000, zzz2200000, True, eg, eh) → LT
new_compare29(zzz24000, zzz2200000, True, bfe, bff, bfg) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), bec, app(app(ty_Either, cbh), cca)) → new_esEs4(zzz5000, zzz4000, cbh, cca)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_compare25(zzz24000, zzz2200000, True) → EQ
new_esEs23(zzz5000, zzz4000, app(ty_Ratio, cfh)) → new_esEs20(zzz5000, zzz4000, cfh)
new_sizeFM0(Branch(zzz39340, zzz39341, zzz39342, zzz39343, zzz39344), h, ba, bb) → zzz39342
new_ltEs19(zzz24001, zzz2200001, ty_Ordering) → new_ltEs8(zzz24001, zzz2200001)
new_esEs22(zzz5001, zzz4001, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs6(zzz5001, zzz4001, bdf, bdg, bdh)
new_esEs23(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_mkBalBranch6MkBalBranch11(zzz3930, zzz3931, zzz4320, zzz4321, zzz4322, zzz4323, zzz4324, zzz3934, True, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz4320, zzz4321, zzz4323, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz3930, zzz3931, zzz4324, zzz3934, app(app(ty_Either, h), ba), bb), app(app(ty_Either, h), ba), bb)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, caf), cag), bed) → new_esEs4(zzz5000, zzz4000, caf, cag)
new_sizeFM1(Branch(zzz6700, zzz6701, zzz6702, zzz6703, zzz6704), cad, cae) → zzz6702
new_splitGT11(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, False, h, ba, bd) → zzz3164
new_esEs28(zzz24000, zzz2200000, ty_Char) → new_esEs15(zzz24000, zzz2200000)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, app(ty_Ratio, cch)) → new_esEs20(zzz5000, zzz4000, cch)
new_compare13(zzz24000, zzz2200000, False) → GT
new_esEs10(zzz5001, zzz4001, app(ty_[], hc)) → new_esEs18(zzz5001, zzz4001, hc)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bed) → new_esEs15(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, app(ty_Maybe, bgc)) → new_lt17(zzz24001, zzz2200001, bgc)
new_esEs21(zzz5000, zzz4000, ty_Char) → new_esEs15(zzz5000, zzz4000)
new_esEs16(False, True) → False
new_esEs16(True, False) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bed) → new_esEs13(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_splitGT4(Branch(zzz35240, zzz35241, zzz35242, zzz35243, zzz35244), zzz353, db, dc, df) → new_splitGT22(zzz35240, zzz35241, zzz35242, zzz35243, zzz35244, zzz353, new_gt0(zzz353, zzz35240, db, dc), db, dc, df)
new_compare16(zzz24000, zzz2200000, True) → LT
new_esEs21(zzz5000, zzz4000, app(ty_[], bcc)) → new_esEs18(zzz5000, zzz4000, bcc)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs20(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bef) → new_asAs(new_esEs26(zzz5000, zzz4000, bef), new_esEs27(zzz5001, zzz4001, bef))
new_esEs24(zzz24000, zzz2200000, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(zzz24000, zzz2200000, bfe, bff, bfg)
new_lt7(zzz24000, zzz2200000) → new_esEs8(new_compare7(zzz24000, zzz2200000), LT)
new_esEs21(zzz5000, zzz4000, app(app(ty_@2, bca), bcb)) → new_esEs7(zzz5000, zzz4000, bca, bcb)
new_esEs28(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_ltEs20(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_primPlusInt2(EmptyFM, zzz3930, zzz3931, zzz3934, h, ba, bb) → new_primPlusInt0(Zero, new_mkBalBranch6Size_r(zzz3930, zzz3931, EmptyFM, zzz3934, h, ba, bb))
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_splitLT21(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, True, h, ba, bd) → new_splitLT3(zzz3153, zzz317, h, ba, bd)
new_esEs11(zzz5002, zzz4002, ty_Int) → new_esEs19(zzz5002, zzz4002)
new_esEs8(EQ, EQ) → True
new_primPlusInt0(zzz43220, Neg(zzz5550)) → new_primMinusNat0(zzz43220, zzz5550)
new_esEs14(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_splitLT22(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, False, db, dc, df) → new_splitLT12(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, new_gt0(zzz353, zzz3510, db, dc), db, dc, df)
new_primPlusNat1(Zero, zzz400000) → Succ(zzz400000)
new_esEs30(zzz500, zzz400, ty_Bool) → new_esEs16(zzz500, zzz400)
new_compare32(zzz24000, zzz2200000, ty_Int) → new_compare18(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, ty_Ordering) → new_lt15(zzz24000, zzz2200000)
new_esEs23(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare24(zzz24000, zzz2200000, True, eg, eh) → EQ
new_esEs21(zzz5000, zzz4000, app(app(ty_Either, bbg), bbh)) → new_esEs4(zzz5000, zzz4000, bbg, bbh)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, app(app(ty_Either, dfd), dfe)) → new_ltEs16(zzz24000, zzz2200000, dfd, dfe)
new_ltEs20(zzz2400, zzz220000, app(ty_Ratio, ceg)) → new_ltEs5(zzz2400, zzz220000, ceg)
new_compare30(zzz24000, zzz2200000) → new_compare25(zzz24000, zzz2200000, new_esEs8(zzz24000, zzz2200000))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_splitGT11(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, True, h, ba, bd) → new_mkVBalBranch0(zzz3160, zzz3161, new_splitGT3(zzz3163, zzz317, h, ba, bd), zzz3164, h, ba, bd)
new_ltEs13(zzz2400, zzz220000) → new_fsEs(new_compare15(zzz2400, zzz220000))
new_esEs29(zzz500, zzz400, ty_Bool) → new_esEs16(zzz500, zzz400)
new_esEs22(zzz5001, zzz4001, app(ty_Ratio, bea)) → new_esEs20(zzz5001, zzz4001, bea)
new_ltEs20(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare32(zzz24000, zzz2200000, app(ty_[], cdc)) → new_compare0(zzz24000, zzz2200000, cdc)
new_esEs21(zzz5000, zzz4000, app(ty_Ratio, bcg)) → new_esEs20(zzz5000, zzz4000, bcg)
new_lt13(zzz24000, zzz2200000, app(app(ty_Either, bfc), bfd)) → new_lt11(zzz24000, zzz2200000, bfc, bfd)
new_esEs28(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, app(app(ty_@2, dcb), dcc)) → new_esEs7(zzz24000, zzz2200000, dcb, dcc)
new_addToFM_C20(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, True, db, dc, df) → new_mkBalBranch(zzz4870, zzz4871, new_addToFM_C0(zzz4873, zzz3510, zzz3511, db, dc, df), zzz4874, db, dc, df)
new_primCmpNat0(Succ(zzz240000), Succ(zzz22000000)) → new_primCmpNat0(zzz240000, zzz22000000)
new_primMinusNat0(Succ(zzz432200), Zero) → Pos(Succ(zzz432200))
new_mkVBalBranch3MkVBalBranch20(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, db, dc, df) → new_mkBalBranch(zzz4870, zzz4871, new_mkVBalBranch0(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz4873, db, dc, df), zzz4874, db, dc, df)
new_splitGT12(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, False, db, dc, df) → zzz3524
new_esEs26(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_lt12(zzz24001, zzz2200001, ty_Ordering) → new_lt15(zzz24001, zzz2200001)
new_gt1(zzz317, zzz323, h, ba) → new_esEs8(new_compare19(Left(zzz317), zzz323, h, ba), GT)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Int, ddh) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Integer, ddh) → new_ltEs6(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bed) → new_esEs17(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_Bool) → new_esEs16(zzz5002, zzz4002)
new_esEs25(zzz24001, zzz2200001, app(ty_Maybe, bgc)) → new_esEs5(zzz24001, zzz2200001, bgc)
new_mkBalBranch6MkBalBranch01(zzz3930, zzz3931, zzz432, zzz39340, zzz39341, zzz39342, EmptyFM, zzz39344, False, h, ba, bb) → error([])
new_esEs9(zzz5000, zzz4000, app(app(ty_@2, fg), fh)) → new_esEs7(zzz5000, zzz4000, fg, fh)
new_esEs21(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs29(zzz500, zzz400, app(ty_Maybe, beg)) → new_esEs5(zzz500, zzz400, beg)
new_ltEs19(zzz24001, zzz2200001, ty_Bool) → new_ltEs14(zzz24001, zzz2200001)
new_compare8(Float(zzz24000, zzz24001), Float(zzz2200000, zzz2200001)) → new_compare18(new_sr(zzz24000, zzz2200000), new_sr(zzz24001, zzz2200001))
new_esEs13(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs19(new_sr(zzz5000, zzz4000), new_sr(zzz5001, zzz4001))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bed) → new_esEs12(zzz5000, zzz4000)
new_ltEs21(zzz2400, zzz220000, app(ty_Ratio, ebb)) → new_ltEs5(zzz2400, zzz220000, ebb)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_compare25(zzz24000, zzz2200000, False) → new_compare13(zzz24000, zzz2200000, new_ltEs8(zzz24000, zzz2200000))
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_mkBalBranch6MkBalBranch5(zzz3930, zzz3931, zzz432, zzz3934, False, h, ba, bb) → new_mkBalBranch6MkBalBranch4(zzz3930, zzz3931, zzz432, zzz3934, new_gt2(new_mkBalBranch6Size_r(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb))), h, ba, bb)
new_lt13(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_compare14(Integer(zzz24000), Integer(zzz2200000)) → new_primCmpInt(zzz24000, zzz2200000)
new_ltEs10(@3(zzz24000, zzz24001, zzz24002), @3(zzz2200000, zzz2200001, zzz2200002), beh, bfa, bfb) → new_pePe(new_lt13(zzz24000, zzz2200000, beh), new_asAs(new_esEs24(zzz24000, zzz2200000, beh), new_pePe(new_lt12(zzz24001, zzz2200001, bfa), new_asAs(new_esEs25(zzz24001, zzz2200001, bfa), new_ltEs11(zzz24002, zzz2200002, bfb)))))
new_sizeFM0(EmptyFM, h, ba, bb) → Pos(Zero)
new_esEs29(zzz500, zzz400, ty_@0) → new_esEs12(zzz500, zzz400)
new_lt12(zzz24001, zzz2200001, ty_Double) → new_lt7(zzz24001, zzz2200001)
new_primCompAux00(zzz266, LT) → LT
new_esEs22(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_addToFM_C10(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, True, db, dc, df) → new_mkBalBranch(zzz4870, zzz4871, zzz4873, new_addToFM_C0(zzz4874, zzz3510, zzz3511, db, dc, df), db, dc, df)
new_ltEs21(zzz2400, zzz220000, ty_Float) → new_ltEs18(zzz2400, zzz220000)
new_mkBalBranch6MkBalBranch11(zzz3930, zzz3931, zzz4320, zzz4321, zzz4322, zzz4323, EmptyFM, zzz3934, False, h, ba, bb) → error([])
new_esEs24(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, app(app(ty_@2, ha), hb)) → new_esEs7(zzz5001, zzz4001, ha, hb)
new_esEs22(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Double, ddh) → new_ltEs15(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Float) → new_ltEs18(zzz24000, zzz2200000)
new_esEs28(zzz24000, zzz2200000, ty_Ordering) → new_esEs8(zzz24000, zzz2200000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_esEs10(zzz5001, zzz4001, ty_Char) → new_esEs15(zzz5001, zzz4001)
new_esEs11(zzz5002, zzz4002, app(ty_[], bae)) → new_esEs18(zzz5002, zzz4002, bae)
new_primPlusNat0(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat0(Succ(zzz20100), Zero) → Succ(zzz20100)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, app(app(app(ty_@3, dfg), dfh), dga)) → new_ltEs10(zzz24000, zzz2200000, dfg, dfh, dga)
new_esEs21(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz240000), Zero) → GT
new_lt20(zzz24000, zzz2200000, app(app(ty_@2, dcb), dcc)) → new_lt4(zzz24000, zzz2200000, dcb, dcc)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz220000))) → LT
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Bool) → new_ltEs14(zzz24000, zzz2200000)
new_compare11(zzz235, zzz236, True, cee, cef) → LT
new_esEs21(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_esEs11(zzz5002, zzz4002, ty_@0) → new_esEs12(zzz5002, zzz4002)
new_compare13(zzz24000, zzz2200000, True) → LT
new_sr0(Integer(zzz240000), Integer(zzz22000010)) → Integer(new_primMulInt(zzz240000, zzz22000010))
new_ltEs20(zzz2400, zzz220000, ty_Char) → new_ltEs13(zzz2400, zzz220000)
new_compare26(zzz24000, zzz2200000, bfe, bff, bfg) → new_compare29(zzz24000, zzz2200000, new_esEs6(zzz24000, zzz2200000, bfe, bff, bfg), bfe, bff, bfg)
new_lt6(zzz24000, zzz2200000, bbc) → new_esEs8(new_compare0(zzz24000, zzz2200000, bbc), LT)
new_ltEs20(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_lt19(zzz240, zzz22000) → new_esEs8(new_compare18(zzz240, zzz22000), LT)
new_ltEs9(zzz2400, zzz220000) → new_fsEs(new_compare18(zzz2400, zzz220000))
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, app(ty_Maybe, dff)) → new_ltEs17(zzz24000, zzz2200000, dff)
new_compare210(zzz24000, zzz2200000, True, ef) → EQ
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_splitGT4(EmptyFM, zzz353, db, dc, df) → new_emptyFM(db, dc, df)
new_lt12(zzz24001, zzz2200001, app(ty_Ratio, bha)) → new_lt9(zzz24001, zzz2200001, bha)
new_splitLT11(zzz3150, zzz3151, zzz3152, zzz3153, zzz3154, zzz317, True, h, ba, bd) → new_mkVBalBranch0(zzz3150, zzz3151, zzz3153, new_splitLT3(zzz3154, zzz317, h, ba, bd), h, ba, bd)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_ltEs12(zzz2400, zzz220000, cdb) → new_fsEs(new_compare0(zzz2400, zzz220000, cdb))
new_mkVBalBranch3MkVBalBranch10(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, True, db, dc, df) → new_mkBalBranch(zzz35130, zzz35131, zzz35133, new_mkVBalBranch0(zzz3510, zzz3511, zzz35134, Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), db, dc, df), db, dc, df)
new_ltEs6(zzz2400, zzz220000) → new_fsEs(new_compare14(zzz2400, zzz220000))
new_esEs22(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz2400)), Neg(Zero)) → LT
new_lt12(zzz24001, zzz2200001, ty_Float) → new_lt8(zzz24001, zzz2200001)
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_@2, deg), deh), ddh) → new_ltEs7(zzz24000, zzz2200000, deg, deh)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz220000))) → new_primCmpNat0(Zero, Succ(zzz220000))
new_primCompAux00(zzz266, EQ) → zzz266
new_esEs11(zzz5002, zzz4002, ty_Float) → new_esEs14(zzz5002, zzz4002)
new_splitGT21(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, False, h, ba, bd) → new_splitGT11(zzz3160, zzz3161, zzz3162, zzz3163, zzz3164, zzz317, new_lt11(Left(zzz317), zzz3160, h, ba), h, ba, bd)
new_lt4(zzz24000, zzz2200000, eg, eh) → new_esEs8(new_compare5(zzz24000, zzz2200000, eg, eh), LT)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_@0) → new_ltEs4(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, ty_Integer) → new_compare14(zzz24000, zzz2200000)
new_ltEs8(GT, LT) → False
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_splitGT3(EmptyFM, zzz317, h, ba, bd) → new_emptyFM(h, ba, bd)
new_primPlusInt1(zzz43220, Neg(zzz5560)) → Neg(new_primPlusNat0(zzz43220, zzz5560))
new_esEs9(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_compare17(zzz24000, zzz2200000, False, eg, eh) → GT
new_intersectFM_C2Gts(zzz312, zzz313, zzz314, zzz315, zzz316, zzz317, h, ba, bd) → new_splitGT21(Left(zzz312), zzz313, zzz314, zzz315, zzz316, zzz317, new_gt1(zzz317, Left(zzz312), h, ba), h, ba, bd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_esEs7(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), bbe, bbf) → new_asAs(new_esEs21(zzz5000, zzz4000, bbe), new_esEs22(zzz5001, zzz4001, bbf))
new_esEs9(zzz5000, zzz4000, app(app(ty_Either, fd), ff)) → new_esEs4(zzz5000, zzz4000, fd, ff)
new_esEs9(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs23(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs9(zzz5000, zzz4000, ty_Float) → new_esEs14(zzz5000, zzz4000)
new_not(False) → True
new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df) → new_sizeFM(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, db, dc, df)
new_esEs21(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs30(zzz500, zzz400, app(app(ty_@2, daa), dab)) → new_esEs7(zzz500, zzz400, daa, dab)
new_compare12(zzz24000, zzz2200000, False, bfe, bff, bfg) → GT
new_esEs25(zzz24001, zzz2200001, ty_Double) → new_esEs13(zzz24001, zzz2200001)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, app(ty_[], ccd)) → new_esEs18(zzz5000, zzz4000, ccd)
new_esEs30(zzz500, zzz400, app(app(ty_Either, chg), chh)) → new_esEs4(zzz500, zzz400, chg, chh)
new_ltEs16(Left(zzz24000), Right(zzz2200000), dfb, ddh) → True
new_ltEs15(zzz2400, zzz220000) → new_fsEs(new_compare7(zzz2400, zzz220000))
new_splitGT3(Branch(zzz31640, zzz31641, zzz31642, zzz31643, zzz31644), zzz317, h, ba, bd) → new_splitGT21(zzz31640, zzz31641, zzz31642, zzz31643, zzz31644, zzz317, new_gt(Left(zzz317), zzz31640, h, ba), h, ba, bd)
new_ltEs19(zzz24001, zzz2200001, app(ty_[], dce)) → new_ltEs12(zzz24001, zzz2200001, dce)
new_lt12(zzz24001, zzz2200001, ty_Int) → new_lt19(zzz24001, zzz2200001)
new_splitLT12(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, True, db, dc, df) → new_mkVBalBranch0(zzz3510, zzz3511, zzz3513, new_splitLT4(zzz3514, zzz353, db, dc, df), db, dc, df)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Ordering, ddh) → new_ltEs8(zzz24000, zzz2200000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Ordering) → new_ltEs8(zzz24000, zzz2200000)
new_splitLT22(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, True, db, dc, df) → new_splitLT4(zzz3513, zzz353, db, dc, df)
new_esEs9(zzz5000, zzz4000, app(ty_Maybe, gf)) → new_esEs5(zzz5000, zzz4000, gf)
new_primPlusInt2(Branch(zzz4320, zzz4321, Neg(zzz43220), zzz4323, zzz4324), zzz3930, zzz3931, zzz3934, h, ba, bb) → new_primPlusInt1(zzz43220, new_sizeFM0(zzz3934, h, ba, bb))
new_lt20(zzz24000, zzz2200000, app(ty_Maybe, dbf)) → new_lt17(zzz24000, zzz2200000, dbf)
new_compare0(:(zzz24000, zzz24001), [], cdb) → GT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bed) → new_esEs19(zzz5000, zzz4000)
new_compare32(zzz24000, zzz2200000, app(app(app(ty_@3, cdg), cdh), cea)) → new_compare26(zzz24000, zzz2200000, cdg, cdh, cea)
new_compare28(zzz24000, zzz2200000, True) → EQ
new_splitLT12(zzz3510, zzz3511, zzz3512, zzz3513, zzz3514, zzz353, False, db, dc, df) → zzz3513
new_esEs24(zzz24000, zzz2200000, app(ty_Maybe, ef)) → new_esEs5(zzz24000, zzz2200000, ef)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_lt13(zzz24000, zzz2200000, app(ty_Ratio, bbd)) → new_lt9(zzz24000, zzz2200000, bbd)
new_compare11(zzz235, zzz236, False, cee, cef) → GT
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz2400)), Neg(zzz22000)) → GT
new_ltEs19(zzz24001, zzz2200001, ty_Int) → new_ltEs9(zzz24001, zzz2200001)
new_lt15(zzz24000, zzz2200000) → new_esEs8(new_compare30(zzz24000, zzz2200000), LT)
new_ltEs18(zzz2400, zzz220000) → new_fsEs(new_compare8(zzz2400, zzz220000))
new_ltEs11(zzz24002, zzz2200002, ty_Float) → new_ltEs18(zzz24002, zzz2200002)
new_esEs11(zzz5002, zzz4002, app(ty_Maybe, bbb)) → new_esEs5(zzz5002, zzz4002, bbb)
new_addToFM_C0(Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), zzz3510, zzz3511, db, dc, df) → new_addToFM_C20(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, new_lt11(zzz3510, zzz4870, db, dc), db, dc, df)
new_lt12(zzz24001, zzz2200001, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt18(zzz24001, zzz2200001, bgd, bge, bgf)
new_ltEs19(zzz24001, zzz2200001, ty_@0) → new_ltEs4(zzz24001, zzz2200001)
new_esEs9(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_ltEs11(zzz24002, zzz2200002, app(app(app(ty_@3, bhf), bhg), bhh)) → new_ltEs10(zzz24002, zzz2200002, bhf, bhg, bhh)
new_esEs23(zzz5000, zzz4000, app(app(ty_Either, ceh), cfa)) → new_esEs4(zzz5000, zzz4000, ceh, cfa)
new_esEs22(zzz5001, zzz4001, ty_Double) → new_esEs13(zzz5001, zzz4001)
new_ltEs17(Nothing, Just(zzz2200000), cgd) → True
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkBalBranch6Size_l(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb) → new_sizeFM0(zzz432, h, ba, bb)
new_mkBalBranch6MkBalBranch4(zzz3930, zzz3931, zzz432, EmptyFM, True, h, ba, bb) → error([])
new_esEs29(zzz500, zzz400, ty_Char) → new_esEs15(zzz500, zzz400)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_splitLT4(Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), zzz353, db, dc, df) → new_splitLT22(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz353, new_lt11(Right(zzz353), zzz35130, db, dc), db, dc, df)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Int) → new_ltEs9(zzz24000, zzz2200000)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz24000, zzz2200000, app(app(ty_Either, bfc), bfd)) → new_esEs4(zzz24000, zzz2200000, bfc, bfd)
new_esEs28(zzz24000, zzz2200000, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs6(zzz24000, zzz2200000, dbg, dbh, dca)
new_primPlusInt(Neg(zzz7200), zzz670, zzz671, zzz668, cad, cae) → new_primPlusInt1(zzz7200, new_sizeFM1(zzz671, cad, cae))
new_mkBalBranch6MkBalBranch4(zzz3930, zzz3931, zzz432, zzz3934, False, h, ba, bb) → new_mkBalBranch6MkBalBranch3(zzz3930, zzz3931, zzz432, zzz3934, new_gt2(new_mkBalBranch6Size_l(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb))), h, ba, bb)
new_ltEs21(zzz2400, zzz220000, app(app(ty_@2, eah), eba)) → new_ltEs7(zzz2400, zzz220000, eah, eba)
new_primPlusInt2(Branch(zzz4320, zzz4321, Pos(zzz43220), zzz4323, zzz4324), zzz3930, zzz3931, zzz3934, h, ba, bb) → new_primPlusInt0(zzz43220, new_sizeFM0(zzz3934, h, ba, bb))
new_compare31(zzz24000, zzz2200000, ef) → new_compare210(zzz24000, zzz2200000, new_esEs5(zzz24000, zzz2200000, ef), ef)
new_ltEs17(Nothing, Nothing, cgd) → True
new_ltEs19(zzz24001, zzz2200001, ty_Char) → new_ltEs13(zzz24001, zzz2200001)
new_mkBalBranch(zzz3930, zzz3931, zzz432, zzz3934, h, ba, bb) → new_mkBalBranch6MkBalBranch5(zzz3930, zzz3931, zzz432, zzz3934, new_lt19(new_primPlusInt2(zzz432, zzz3930, zzz3931, zzz3934, h, ba, bb), Pos(Succ(Succ(Zero)))), h, ba, bb)
new_mkBalBranch6MkBalBranch3(zzz3930, zzz3931, EmptyFM, zzz3934, True, h, ba, bb) → error([])
new_primPlusNat1(Succ(zzz2010), zzz400000) → Succ(Succ(new_primPlusNat0(zzz2010, zzz400000)))
new_compare32(zzz24000, zzz2200000, ty_Float) → new_compare8(zzz24000, zzz2200000)
new_mkVBalBranch0(zzz3510, zzz3511, Branch(zzz35130, zzz35131, zzz35132, zzz35133, zzz35134), Branch(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874), db, dc, df) → new_mkVBalBranch3MkVBalBranch20(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df)), new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df)), db, dc, df)
new_lt20(zzz24000, zzz2200000, app(app(ty_Either, dbd), dbe)) → new_lt11(zzz24000, zzz2200000, dbd, dbe)
new_lt13(zzz24000, zzz2200000, app(ty_[], bbc)) → new_lt6(zzz24000, zzz2200000, bbc)
new_lt12(zzz24001, zzz2200001, app(app(ty_Either, bga), bgb)) → new_lt11(zzz24001, zzz2200001, bga, bgb)
new_ltEs19(zzz24001, zzz2200001, app(ty_Maybe, dch)) → new_ltEs17(zzz24001, zzz2200001, dch)
new_compare32(zzz24000, zzz2200000, ty_Char) → new_compare15(zzz24000, zzz2200000)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_[], ddg), ddh) → new_ltEs12(zzz24000, zzz2200000, ddg)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_esEs10(zzz5001, zzz4001, app(ty_Maybe, hh)) → new_esEs5(zzz5001, zzz4001, hh)
new_esEs16(True, True) → True
new_primCmpInt(Neg(Zero), Neg(Succ(zzz220000))) → new_primCmpNat0(Succ(zzz220000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz220000))) → GT
new_esEs24(zzz24000, zzz2200000, ty_Bool) → new_esEs16(zzz24000, zzz2200000)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, dhb), dhc), dhd)) → new_esEs6(zzz5000, zzz4000, dhb, dhc, dhd)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_lt13(zzz24000, zzz2200000, app(app(ty_@2, eg), eh)) → new_lt4(zzz24000, zzz2200000, eg, eh)
new_ltEs21(zzz2400, zzz220000, ty_Integer) → new_ltEs6(zzz2400, zzz220000)
new_esEs10(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_lt16(zzz24000, zzz2200000) → new_esEs8(new_compare14(zzz24000, zzz2200000), LT)
new_emptyFM(bf, bg, bh) → EmptyFM
new_esEs29(zzz500, zzz400, ty_Int) → new_esEs19(zzz500, zzz400)
new_esEs22(zzz5001, zzz4001, ty_@0) → new_esEs12(zzz5001, zzz4001)
new_intersectFM_C2Gts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg) → new_splitGT21(Right(zzz329), zzz330, zzz331, zzz332, zzz333, zzz334, new_gt1(zzz334, Right(zzz329), cc, cd), cc, cd, cg)
new_intersectFM_C2Lts1(zzz348, zzz349, zzz350, zzz351, zzz352, zzz353, db, dc, df) → new_splitLT22(Left(zzz348), zzz349, zzz350, zzz351, zzz352, zzz353, new_lt11(Right(zzz353), Left(zzz348), db, dc), db, dc, df)
new_esEs10(zzz5001, zzz4001, ty_Float) → new_esEs14(zzz5001, zzz4001)
new_mkVBalBranch3MkVBalBranch20(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, False, db, dc, df) → new_mkVBalBranch3MkVBalBranch10(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, zzz3510, zzz3511, new_lt19(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df)), new_mkVBalBranch3Size_l(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz35130, zzz35131, zzz35132, zzz35133, zzz35134, db, dc, df)), db, dc, df)
new_mkBalBranch6MkBalBranch3(zzz3930, zzz3931, zzz432, zzz3934, False, h, ba, bb) → new_mkBranch(Succ(Zero), zzz3930, zzz3931, zzz432, zzz3934, app(app(ty_Either, h), ba), bb)
new_esEs19(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt20(zzz24000, zzz2200000, ty_Char) → new_lt10(zzz24000, zzz2200000)
new_esEs21(zzz5000, zzz4000, ty_Integer) → new_esEs17(zzz5000, zzz4000)
new_esEs28(zzz24000, zzz2200000, app(ty_[], dbc)) → new_esEs18(zzz24000, zzz2200000, dbc)
new_esEs30(zzz500, zzz400, app(ty_[], dac)) → new_esEs18(zzz500, zzz400, dac)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(zzz24001, zzz2200001, ty_Float) → new_ltEs18(zzz24001, zzz2200001)
new_compare29(zzz24000, zzz2200000, False, bfe, bff, bfg) → new_compare12(zzz24000, zzz2200000, new_ltEs10(zzz24000, zzz2200000, bfe, bff, bfg), bfe, bff, bfg)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_asAs(False, zzz230) → False
new_mkVBalBranch0(zzz3510, zzz3511, EmptyFM, zzz487, db, dc, df) → new_addToFM(zzz487, zzz3510, zzz3511, db, dc, df)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_@2, ddd), dde)) → new_ltEs7(zzz24001, zzz2200001, ddd, dde)
new_esEs10(zzz5001, zzz4001, app(app(app(ty_@3, hd), he), hf)) → new_esEs6(zzz5001, zzz4001, hd, he, hf)
new_gt(zzz3510, zzz4870, db, dc) → new_esEs8(new_compare19(zzz3510, zzz4870, db, dc), GT)
new_esEs9(zzz5000, zzz4000, ty_Double) → new_esEs13(zzz5000, zzz4000)
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM1(EmptyFM, cad, cae) → Pos(Zero)
new_compare32(zzz24000, zzz2200000, app(ty_Maybe, cdf)) → new_compare31(zzz24000, zzz2200000, cdf)
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_esEs24(zzz24000, zzz2200000, ty_Double) → new_esEs13(zzz24000, zzz2200000)
new_esEs18([], [], bee) → True
new_esEs11(zzz5002, zzz4002, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5002, zzz4002, baa, bab)
new_esEs23(zzz5000, zzz4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(zzz5000, zzz4000, cfe, cff, cfg)
new_esEs21(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Integer) → new_ltEs6(zzz24000, zzz2200000)
new_compare32(zzz24000, zzz2200000, app(app(ty_Either, cdd), cde)) → new_compare19(zzz24000, zzz2200000, cdd, cde)
new_mkBalBranch6MkBalBranch4(zzz3930, zzz3931, zzz432, Branch(zzz39340, zzz39341, zzz39342, zzz39343, zzz39344), True, h, ba, bb) → new_mkBalBranch6MkBalBranch01(zzz3930, zzz3931, zzz432, zzz39340, zzz39341, zzz39342, zzz39343, zzz39344, new_lt19(new_sizeFM0(zzz39343, h, ba, bb), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM0(zzz39344, h, ba, bb))), h, ba, bb)
new_esEs23(zzz5000, zzz4000, app(app(ty_@2, cfb), cfc)) → new_esEs7(zzz5000, zzz4000, cfb, cfc)
new_ltEs17(Just(zzz24000), Just(zzz2200000), ty_Char) → new_ltEs13(zzz24000, zzz2200000)
new_ltEs21(zzz2400, zzz220000, ty_Bool) → new_ltEs14(zzz2400, zzz220000)
new_esEs29(zzz500, zzz400, ty_Double) → new_esEs13(zzz500, zzz400)
new_ltEs21(zzz2400, zzz220000, ty_Double) → new_ltEs15(zzz2400, zzz220000)
new_compare9(:%(zzz24000, zzz24001), :%(zzz2200000, zzz2200001), ty_Int) → new_compare18(new_sr(zzz24000, zzz2200001), new_sr(zzz2200000, zzz24001))
new_splitLT3(EmptyFM, zzz317, h, ba, bd) → new_emptyFM(h, ba, bd)
new_lt20(zzz24000, zzz2200000, ty_Float) → new_lt8(zzz24000, zzz2200000)
new_esEs24(zzz24000, zzz2200000, ty_Integer) → new_esEs17(zzz24000, zzz2200000)
new_esEs30(zzz500, zzz400, ty_Float) → new_esEs14(zzz500, zzz400)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, cbg), bed) → new_esEs5(zzz5000, zzz4000, cbg)
new_esEs28(zzz24000, zzz2200000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz24000, zzz2200000, dbd, dbe)
new_compare211(Right(zzz2400), Left(zzz220000), False, cgb, cgc) → GT
new_esEs23(zzz5000, zzz4000, app(ty_Maybe, cga)) → new_esEs5(zzz5000, zzz4000, cga)
new_esEs29(zzz500, zzz400, ty_Float) → new_esEs14(zzz500, zzz400)
new_esEs25(zzz24001, zzz2200001, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs6(zzz24001, zzz2200001, bgd, bge, bgf)
new_lt13(zzz24000, zzz2200000, ty_Double) → new_lt7(zzz24000, zzz2200000)
new_esEs10(zzz5001, zzz4001, ty_Bool) → new_esEs16(zzz5001, zzz4001)
new_mkBalBranch6MkBalBranch3(zzz3930, zzz3931, Branch(zzz4320, zzz4321, zzz4322, zzz4323, zzz4324), zzz3934, True, h, ba, bb) → new_mkBalBranch6MkBalBranch11(zzz3930, zzz3931, zzz4320, zzz4321, zzz4322, zzz4323, zzz4324, zzz3934, new_lt19(new_sizeFM0(zzz4324, h, ba, bb), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM0(zzz4323, h, ba, bb))), h, ba, bb)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cbb), bed) → new_esEs18(zzz5000, zzz4000, cbb)
new_ltEs11(zzz24002, zzz2200002, ty_Double) → new_ltEs15(zzz24002, zzz2200002)
new_compare211(Left(zzz2400), Right(zzz220000), False, cgb, cgc) → LT
new_ltEs11(zzz24002, zzz2200002, app(app(ty_@2, caa), cab)) → new_ltEs7(zzz24002, zzz2200002, caa, cab)
new_esEs23(zzz5000, zzz4000, ty_@0) → new_esEs12(zzz5000, zzz4000)
new_ltEs8(LT, GT) → True
new_esEs16(False, False) → True
new_esEs5(Nothing, Just(zzz4000), beg) → False
new_esEs5(Just(zzz5000), Nothing, beg) → False
new_esEs10(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_primMinusNat0(Zero, Succ(zzz55500)) → Neg(Succ(zzz55500))
new_ltEs16(Right(zzz24000), Left(zzz2200000), dfb, ddh) → False
new_compare211(zzz240, zzz22000, True, cgb, cgc) → EQ
new_lt5(zzz24000, zzz2200000) → new_esEs8(new_compare6(zzz24000, zzz2200000), LT)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cah), cba), bed) → new_esEs7(zzz5000, zzz4000, cah, cba)
new_sizeFM(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, h, ba, bb) → zzz3932
new_esEs28(zzz24000, zzz2200000, app(ty_Ratio, dcd)) → new_esEs20(zzz24000, zzz2200000, dcd)
new_esEs25(zzz24001, zzz2200001, ty_Char) → new_esEs15(zzz24001, zzz2200001)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Zero)) → GT
new_esEs22(zzz5001, zzz4001, ty_Int) → new_esEs19(zzz5001, zzz4001)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, app(ty_Ratio, dgd)) → new_ltEs5(zzz24000, zzz2200000, dgd)
new_splitGT22(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, False, db, dc, df) → new_splitGT12(zzz3520, zzz3521, zzz3522, zzz3523, zzz3524, zzz353, new_lt11(Right(zzz353), zzz3520, db, dc), db, dc, df)
new_ltEs16(Left(zzz24000), Left(zzz2200000), ty_Char, ddh) → new_ltEs13(zzz24000, zzz2200000)
new_ltEs16(Right(zzz24000), Right(zzz2200000), dfb, ty_Double) → new_ltEs15(zzz24000, zzz2200000)
new_lt20(zzz24000, zzz2200000, ty_Int) → new_lt19(zzz24000, zzz2200000)
new_primCmpInt(Pos(Succ(zzz2400)), Pos(Succ(zzz220000))) → new_primCmpNat0(zzz2400, zzz220000)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(app(ty_@2, chd), che)) → new_ltEs7(zzz24000, zzz2200000, chd, che)
new_intersectFM_C2Lts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed) → new_splitLT22(Right(zzz365), zzz366, zzz367, zzz368, zzz369, zzz370, new_lt11(Right(zzz370), Right(zzz365), dh, ea), dh, ea, ed)
new_esEs26(zzz5000, zzz4000, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs5(Nothing, Nothing, beg) → True
new_esEs28(zzz24000, zzz2200000, app(ty_Maybe, dbf)) → new_esEs5(zzz24000, zzz2200000, dbf)
new_esEs23(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), bec, ty_Int) → new_esEs19(zzz5000, zzz4000)
new_esEs29(zzz500, zzz400, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz500, zzz400, fa, fb, fc)
new_esEs22(zzz5001, zzz4001, ty_Integer) → new_esEs17(zzz5001, zzz4001)
new_esEs9(zzz5000, zzz4000, app(ty_Ratio, ge)) → new_esEs20(zzz5000, zzz4000, ge)
new_ltEs11(zzz24002, zzz2200002, app(app(ty_Either, bhc), bhd)) → new_ltEs16(zzz24002, zzz2200002, bhc, bhd)
new_ltEs21(zzz2400, zzz220000, app(app(app(ty_@3, eae), eaf), eag)) → new_ltEs10(zzz2400, zzz220000, eae, eaf, eag)
new_ltEs19(zzz24001, zzz2200001, ty_Double) → new_ltEs15(zzz24001, zzz2200001)
new_compare5(zzz24000, zzz2200000, eg, eh) → new_compare24(zzz24000, zzz2200000, new_esEs7(zzz24000, zzz2200000, eg, eh), eg, eh)
new_esEs30(zzz500, zzz400, ty_Ordering) → new_esEs8(zzz500, zzz400)
new_ltEs17(Just(zzz24000), Just(zzz2200000), app(ty_Maybe, cgh)) → new_ltEs17(zzz24000, zzz2200000, cgh)
new_esEs10(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_primPlusNat0(Succ(zzz20100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat0(zzz20100, zzz4000000)))
new_esEs22(zzz5001, zzz4001, app(ty_Maybe, beb)) → new_esEs5(zzz5001, zzz4001, beb)
new_ltEs8(LT, LT) → True
new_esEs21(zzz5000, zzz4000, app(ty_Maybe, bch)) → new_esEs5(zzz5000, zzz4000, bch)
new_esEs9(zzz5000, zzz4000, app(app(app(ty_@3, gb), gc), gd)) → new_esEs6(zzz5000, zzz4000, gb, gc, gd)
new_esEs11(zzz5002, zzz4002, ty_Integer) → new_esEs17(zzz5002, zzz4002)
new_esEs29(zzz500, zzz400, app(ty_[], bee)) → new_esEs18(zzz500, zzz400, bee)
new_compare0([], :(zzz2200000, zzz2200001), cdb) → LT
new_esEs21(zzz5000, zzz4000, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs6(zzz5000, zzz4000, bcd, bce, bcf)
new_intersectFM_C2Lts0(zzz329, zzz330, zzz331, zzz332, zzz333, zzz334, cc, cd, cg) → new_splitLT21(Right(zzz329), zzz330, zzz331, zzz332, zzz333, zzz334, new_lt11(Left(zzz334), Right(zzz329), cc, cd), cc, cd, cg)
new_asAs(True, zzz230) → zzz230
new_ltEs11(zzz24002, zzz2200002, ty_Integer) → new_ltEs6(zzz24002, zzz2200002)
new_esEs30(zzz500, zzz400, ty_Integer) → new_esEs17(zzz500, zzz400)
new_esEs4(Right(zzz5000), Left(zzz4000), bec, bed) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bec, bed) → False
new_lt11(zzz240, zzz22000, cgb, cgc) → new_esEs8(new_compare19(zzz240, zzz22000, cgb, cgc), LT)
new_esEs9(zzz5000, zzz4000, ty_Bool) → new_esEs16(zzz5000, zzz4000)
new_esEs30(zzz500, zzz400, app(ty_Maybe, dah)) → new_esEs5(zzz500, zzz400, dah)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dgg), dgh)) → new_esEs7(zzz5000, zzz4000, dgg, dgh)
new_lt8(zzz24000, zzz2200000) → new_esEs8(new_compare8(zzz24000, zzz2200000), LT)
new_esEs24(zzz24000, zzz2200000, ty_Int) → new_esEs19(zzz24000, zzz2200000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cbc), cbd), cbe), bed) → new_esEs6(zzz5000, zzz4000, cbc, cbd, cbe)
new_lt12(zzz24001, zzz2200001, app(ty_[], bfh)) → new_lt6(zzz24001, zzz2200001, bfh)
new_fsEs(zzz247) → new_not(new_esEs8(zzz247, GT))
new_mkBalBranch6MkBalBranch5(zzz3930, zzz3931, zzz432, zzz3934, True, h, ba, bb) → new_mkBranch(Zero, zzz3930, zzz3931, zzz432, zzz3934, app(app(ty_Either, h), ba), bb)
new_primPlusInt(Pos(zzz7200), zzz670, zzz671, zzz668, cad, cae) → new_primPlusInt0(zzz7200, new_sizeFM1(zzz671, cad, cae))
new_compare19(zzz240, zzz22000, cgb, cgc) → new_compare211(zzz240, zzz22000, new_esEs4(zzz240, zzz22000, cgb, cgc), cgb, cgc)
new_addToFM_C10(zzz4870, zzz4871, zzz4872, zzz4873, zzz4874, zzz3510, zzz3511, False, db, dc, df) → Branch(zzz3510, zzz3511, zzz4872, zzz4873, zzz4874)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(ty_Either, dea), deb), ddh) → new_ltEs16(zzz24000, zzz2200000, dea, deb)
new_esEs24(zzz24000, zzz2200000, app(ty_Ratio, bbd)) → new_esEs20(zzz24000, zzz2200000, bbd)
new_lt12(zzz24001, zzz2200001, ty_Char) → new_lt10(zzz24001, zzz2200001)
new_ltEs20(zzz2400, zzz220000, app(app(app(ty_@3, beh), bfa), bfb)) → new_ltEs10(zzz2400, zzz220000, beh, bfa, bfb)
new_ltEs5(zzz2400, zzz220000, ceg) → new_fsEs(new_compare9(zzz2400, zzz220000, ceg))
new_esEs5(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs19(zzz5000, zzz4000)
new_lt13(zzz24000, zzz2200000, app(app(app(ty_@3, bfe), bff), bfg)) → new_lt18(zzz24000, zzz2200000, bfe, bff, bfg)
new_splitLT3(Branch(zzz31530, zzz31531, zzz31532, zzz31533, zzz31534), zzz317, h, ba, bd) → new_splitLT21(zzz31530, zzz31531, zzz31532, zzz31533, zzz31534, zzz317, new_lt11(Left(zzz317), zzz31530, h, ba), h, ba, bd)
new_ltEs19(zzz24001, zzz2200001, app(app(app(ty_@3, dda), ddb), ddc)) → new_ltEs10(zzz24001, zzz2200001, dda, ddb, ddc)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), fa, fb, fc) → new_asAs(new_esEs9(zzz5000, zzz4000, fa), new_asAs(new_esEs10(zzz5001, zzz4001, fb), new_esEs11(zzz5002, zzz4002, fc)))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bed) → new_esEs16(zzz5000, zzz4000)
new_ltEs11(zzz24002, zzz2200002, app(ty_Maybe, bhe)) → new_ltEs17(zzz24002, zzz2200002, bhe)
new_esEs23(zzz5000, zzz4000, app(ty_[], cfd)) → new_esEs18(zzz5000, zzz4000, cfd)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(ty_Ratio, dfa), ddh) → new_ltEs5(zzz24000, zzz2200000, dfa)
new_primCompAux00(zzz266, GT) → GT
new_esEs30(zzz500, zzz400, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(zzz500, zzz400, dad, dae, daf)
new_esEs25(zzz24001, zzz2200001, ty_Float) → new_esEs14(zzz24001, zzz2200001)
new_ltEs19(zzz24001, zzz2200001, app(app(ty_Either, dcf), dcg)) → new_ltEs16(zzz24001, zzz2200001, dcf, dcg)
new_esEs5(Just(zzz5000), Just(zzz4000), app(ty_[], dha)) → new_esEs18(zzz5000, zzz4000, dha)
new_ltEs21(zzz2400, zzz220000, app(app(ty_Either, eab), eac)) → new_ltEs16(zzz2400, zzz220000, eab, eac)
new_esEs5(Just(zzz5000), Just(zzz4000), app(app(ty_Either, dge), dgf)) → new_esEs4(zzz5000, zzz4000, dge, dgf)
new_ltEs16(Left(zzz24000), Left(zzz2200000), app(app(app(ty_@3, ded), dee), def), ddh) → new_ltEs10(zzz24000, zzz2200000, ded, dee, def)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs29(zzz500, zzz400, ty_Ordering) → new_esEs8(zzz500, zzz400)
new_lt12(zzz24001, zzz2200001, ty_Integer) → new_lt16(zzz24001, zzz2200001)
new_mkBalBranch6MkBalBranch11(zzz3930, zzz3931, zzz4320, zzz4321, zzz4322, zzz4323, Branch(zzz43240, zzz43241, zzz43242, zzz43243, zzz43244), zzz3934, False, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz43240, zzz43241, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz4320, zzz4321, zzz4323, zzz43243, app(app(ty_Either, h), ba), bb), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz3930, zzz3931, zzz43244, zzz3934, app(app(ty_Either, h), ba), bb), app(app(ty_Either, h), ba), bb)
new_intersectFM_C2Gts2(zzz365, zzz366, zzz367, zzz368, zzz369, zzz370, dh, ea, ed) → new_splitGT22(Right(zzz365), zzz366, zzz367, zzz368, zzz369, zzz370, new_gt0(zzz370, Right(zzz365), dh, ea), dh, ea, ed)
new_esEs24(zzz24000, zzz2200000, ty_@0) → new_esEs12(zzz24000, zzz2200000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(zzz24001, zzz2200001, app(ty_Ratio, bha)) → new_esEs20(zzz24001, zzz2200001, bha)
new_esEs30(zzz500, zzz400, ty_Char) → new_esEs15(zzz500, zzz400)
new_ltEs11(zzz24002, zzz2200002, ty_Bool) → new_ltEs14(zzz24002, zzz2200002)
new_primCmpInt(Neg(Succ(zzz2400)), Pos(zzz22000)) → LT
new_compare16(zzz24000, zzz2200000, False) → GT
new_not(True) → False
new_primMinusNat0(Succ(zzz432200), Succ(zzz55500)) → new_primMinusNat0(zzz432200, zzz55500)

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Ordering)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_lt13(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusInt1(x0, Pos(x1))
new_esEs18([], :(x0, x1), x2)
new_mkVBalBranch3MkVBalBranch20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13, x14)
new_addToFM(x0, x1, x2, x3, x4, x5)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_primMinusNat0(Zero, Zero)
new_ltEs16(Left(x0), Left(x1), ty_Int, x2)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_compare16(x0, x1, True)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_splitGT21(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(Right(x0), Right(x1), x2, ty_Double)
new_splitGT22(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_esEs22(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(EQ, EQ)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primMulInt(Neg(x0), Neg(x1))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_splitLT21(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_splitLT11(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs11(x0, x1, app(ty_[], x2))
new_compare30(x0, x1)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_esEs21(x0, x1, ty_Integer)
new_splitGT12(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_splitGT12(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_compare0([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_splitGT3(EmptyFM, x0, x1, x2, x3)
new_ltEs21(x0, x1, ty_Bool)
new_splitGT21(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_Bool)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5, x6)
new_lt13(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs15(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Int)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_compare18(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_@0)
new_ltEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare32(x0, x1, app(ty_Maybe, x2))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs29(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_splitGT3(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_esEs8(GT, GT)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs30(x0, x1, ty_Int)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_compare13(x0, x1, True)
new_lt6(x0, x1, x2)
new_ltEs18(x0, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs5(Nothing, Nothing, x0)
new_esEs10(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(LT, LT)
new_ltEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(ty_[], x2))
new_splitLT3(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_esEs25(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Ordering)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs16(True, False)
new_esEs16(False, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch3(x0, x1, Branch(x2, x3, x4, x5, x6), x7, True, x8, x9, x10)
new_esEs5(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Float)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Ordering)
new_compare25(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs16(True, True)
new_esEs21(x0, x1, ty_Bool)
new_lt16(x0, x1)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_primPlusInt0(x0, Pos(x1))
new_compare28(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_sizeFM1(EmptyFM, x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_mkVBalBranch3MkVBalBranch20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13, x14)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_lt18(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch3(x0, x1, EmptyFM, x2, True, x3, x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_addToFM_C0(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_esEs29(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(@0, @0)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primMulNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Float)
new_emptyFM(x0, x1, x2)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_splitLT12(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_compare211(Right(x0), Right(x1), False, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_ltEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5, x6)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs15(Char(x0), Char(x1))
new_lt15(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare29(x0, x1, False, x2, x3, x4)
new_sIZE_RATIO
new_lt14(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_splitLT22(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare32(x0, x1, ty_Int)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_splitGT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare8(Float(x0, x1), Float(x2, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs30(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusInt1(x0, Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_splitGT11(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_compare211(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt0(x0, x1, x2, x3)
new_compare24(x0, x1, True, x2, x3)
new_esEs23(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_splitLT22(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_compare28(x0, x1, False)
new_esEs22(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_splitGT22(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs10(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, True)
new_ltEs5(x0, x1, x2)
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare17(x0, x1, False, x2, x3)
new_ltEs20(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_asAs(True, x0)
new_ltEs17(Nothing, Nothing, x0)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Zero)
new_ltEs21(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Int)
new_esEs18(:(x0, x1), [], x2)
new_primMinusNat0(Succ(x0), Zero)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_ltEs16(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_Double)
new_lt17(x0, x1, x2)
new_compare16(x0, x1, False)
new_esEs11(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_lt7(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs16(Left(x0), Left(x1), ty_Integer, x2)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Float)
new_esEs18([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt10(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_primCompAux00(x0, GT)
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCompAux00(x0, LT)
new_lt4(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Double)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Char)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13, x14)
new_primCmpNat0(Zero, Succ(x0))
new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_compare210(x0, x1, True, x2)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs29(x0, x1, ty_Float)
new_splitGT4(EmptyFM, x0, x1, x2, x3)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_gt(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, ty_Ordering)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch4(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9, x10)
new_compare32(x0, x1, app(ty_[], x2))
new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Right(x0), Right(x1), x2, ty_Char)
new_lt19(x0, x1)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs13(x0, x1)
new_esEs11(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare14(Integer(x0), Integer(x1))
new_esEs27(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_ltEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare32(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_primPlusInt0(x0, Neg(x1))
new_ltEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, ty_Char)
new_lt8(x0, x1)
new_compare5(x0, x1, x2, x3)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusInt2(Branch(x0, x1, Neg(x2), x3, x4), x5, x6, x7, x8, x9, x10)
new_compare6(@0, @0)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, ty_Ordering)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8, x9)
new_mkVBalBranch0(x0, x1, EmptyFM, x2, x3, x4, x5)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(Right(x0), Left(x1), x2, x3)
new_ltEs16(Left(x0), Right(x1), x2, x3)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_@0)
new_ltEs11(x0, x1, ty_Char)
new_splitLT3(EmptyFM, x0, x1, x2, x3)
new_ltEs8(LT, LT)
new_lt20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_compare10(x0, x1, False, x2)
new_sizeFM1(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, EmptyFM, True, x3, x4, x5)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs21(x0, x1, ty_Float)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_ltEs8(GT, GT)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch10(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13, x14)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitLT4(EmptyFM, x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Char)
new_splitLT11(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Double)
new_ltEs16(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Ordering)
new_splitLT21(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs29(x0, x1, ty_Char)
new_gt2(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1, ty_Char)
new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_splitLT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_compare211(Left(x0), Right(x1), False, x2, x3)
new_compare211(Right(x0), Left(x1), False, x2, x3)
new_compare26(x0, x1, x2, x3, x4)
new_ltEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Double)
new_esEs16(False, False)
new_lt13(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(LT, GT)
new_primPlusInt2(Branch(x0, x1, Pos(x2), x3, x4), x5, x6, x7, x8, x9, x10)
new_ltEs14(True, True)
new_ltEs8(GT, LT)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(x0, x1, x2)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs14(False, False)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_primPlusInt2(EmptyFM, x0, x1, x2, x3, x4, x5)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_ltEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(x0, x1)
new_splitGT11(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_compare32(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, True, x7, x8, x9)
new_esEs22(x0, x1, ty_Char)
new_primMinusNat0(Zero, Succ(x0))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_asAs(False, x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs10(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, True, x7, x8, x9)
new_esEs30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1, x2)
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_compare32(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_pePe(False, x0)
new_esEs28(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitLT12(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_primMinusNat0(Succ(x0), Succ(x1))
new_lt12(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Char)
new_compare110(x0, x1, True, x2, x3)
new_compare29(x0, x1, True, x2, x3, x4)
new_mkBalBranch(x0, x1, x2, x3, x4, x5, x6)
new_compare32(x0, x1, ty_Bool)
new_gt1(x0, x1, x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs17(Just(x0), Nothing, x1)
new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_@0)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_addToFM_C0(EmptyFM, x0, x1, x2, x3, x4)
new_esEs5(Nothing, Just(x0), x1)
new_compare11(x0, x1, False, x2, x3)
new_ltEs16(Left(x0), Left(x1), ty_Float, x2)
new_compare0([], [], x0)
new_primPlusNat1(Zero, x0)
new_mkVBalBranch3MkVBalBranch10(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13, x14)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_@0)
new_lt11(x0, x1, x2, x3)
new_compare13(x0, x1, False)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_@0)
new_compare211(Left(x0), Left(x1), False, x2, x3)
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt13(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_compare31(x0, x1, x2)
new_ltEs16(Left(x0), Left(x1), ty_Double, x2)
new_compare11(x0, x1, True, x2, x3)

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

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