YES 145.202 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 :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a)

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

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

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

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
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 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  ->  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 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_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 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 :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
intersectFM fm1 fm2 = intersectFM_C (\left right ->right) fm1 fm2

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

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

  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



Lambda Reductions:
The following Lambda expression
\leftright→right

is transformed to
intersectFM0 left right = right

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 :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a)

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

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

  
addToFM0 old new = new

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

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

  foldFM :: (c  ->  a  ->  b  ->  b)  ->  b  ->  FiniteMap c a  ->  b
foldFM k z EmptyFM = z
foldFM k z (Branch key elt _ fm_l fm_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 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 :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

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

  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



Case Reductions:
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 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 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 :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a)

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

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

  
addToFM0 old new = new

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

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

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

  foldFM :: (a  ->  b  ->  c  ->  c)  ->  c  ->  FiniteMap a b  ->  c
foldFM k z EmptyFM = z
foldFM k z (Branch key elt _ fm_l fm_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 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 :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  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 :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a)

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

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

  
addToFM0 old new = new

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

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

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

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

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

  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 :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

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



Replaced joker patterns by fresh variables and removed binding patterns.
Binding Reductions:
The bind variable of the following binding Pattern
fm_l@(Branch vy vz wu wv ww)

is replaced by the following term
Branch vy vz wu wv ww

The bind variable of the following binding Pattern
fm_r@(Branch wy wz xu xv xw)

is replaced by the following term
Branch wy wz xu xv xw

The bind variable of the following binding Pattern
fm_l@(Branch vxz vyu vyv vyw vyx)

is replaced by the following term
Branch vxz vyu vyv vyw vyx

The bind variable of the following binding Pattern
fm_r@(Branch vyz vzu vzv vzw vzx)

is replaced by the following term
Branch vyz vzu vzv vzw vzx



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

mainModule FiniteMap
  ((intersectFM :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char 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 a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt vxw fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vxx 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 wux EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuy 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 vzy vzz EmptyFM) = (key,elt)
findMax (Branch key elt wuu wuv fm_r) = findMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt vwu EmptyFM vwv) = (key,elt)
findMin (Branch key elt vww fm_l vwx) = 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 vvy 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 (zx,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (zy,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,zz) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,vuu) = 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 vy vz wu wv ww) (Branch wy wz xu xv xw) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
 | otherwise = 
glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) where 
size_l = sizeFM (Branch vy vz wu wv ww)
size_r = sizeFM (Branch wy wz xu xv xw)

  intersectFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

  intersectFM_C :: Ord a => (b  ->  c  ->  d)  ->  FiniteMap a b  ->  FiniteMap a c  ->  FiniteMap a d
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 vuv 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 wuw 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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv 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 yu yv yw 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 zw 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 xx 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 vuw vux vuy vuz) = 
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 vvu vvv vvw vvx) = 
let 
smallest_right_key = fst (findMin fm_r)
in key < smallest_right_key
right_size = sizeFM fm_r
unbox :: Int  ->  Int
unbox x = x

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
 | otherwise = 
mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) where 
size_l = sizeFM (Branch vxz vyu vyv vyw vyx)
size_r = sizeFM (Branch vyz vzu vzv vzw vzx)

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch vwy vwz size vxu vxv) = size

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt vw 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 vvz 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 wuz = True



Cond Reductions:
The following Function with conditions
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt vw 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 vw fm_l fm_r) split_key = splitGT3 (Branch key elt vw fm_l fm_r) split_key

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

splitGT0 key elt vw fm_l fm_r split_key True = fm_r

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

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

splitGT4 EmptyFM split_key = emptyFM
splitGT4 wzz xuu = splitGT3 wzz xuu

The following Function with conditions
glueVBal EmptyFM fm2 = fm2
glueVBal fm1 EmptyFM = fm1
glueVBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
 | otherwise
 = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)
where 
size_l  = sizeFM (Branch vy vz wu wv ww)
size_r  = sizeFM (Branch wy wz xu xv xw)

is transformed to
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = 
glueVBal2 vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * size_l < size_r)
where 
glueVBal0 vy vz wu wv ww wy wz xu xv xw True = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)
glueVBal1 vy vz wu wv ww wy wz xu xv xw True = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
glueVBal1 vy vz wu wv ww wy wz xu xv xw False = glueVBal0 vy vz wu wv ww wy wz xu xv xw otherwise
glueVBal2 vy vz wu wv ww wy wz xu xv xw True = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
glueVBal2 vy vz wu wv ww wy wz xu xv xw False = glueVBal1 vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch vy vz wu wv ww)
size_r  = sizeFM (Branch wy wz xu xv xw)

glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xuy xuz = glueVBal3 xuy xuz

glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvv xvw = glueVBal4 xvv xvw

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch yu yv yw 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 yu yv yw fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr)

mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr otherwise

mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch yz zu zv 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 yz zu zv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr)

mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr otherwise

mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R yz zu zv 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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv 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 yu yv yw 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 zw 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 xx 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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr)
mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yu yv yw 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 zw 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 xx 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
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 (zx,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (zy,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,zz) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,vuu) = 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 (zx,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (zy,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,zz) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,vuu) = mid_key2
vv2  = findMax fm1
vv3  = findMin fm2

glueBal3 fm1 EmptyFM = fm1
glueBal3 xwu xwv = glueBal2 xwu xwv

glueBal4 EmptyFM fm2 = fm2
glueBal4 xwx xwy = glueBal3 xwx xwy

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 xxv xxw xxx xxy = addToFM_C3 xxv xxw xxx xxy

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 vuv 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 vuv left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right)

intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right) = 
intersectFM_C1 combiner fm1 split_key elt2 vuv 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 vuv left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 vuv 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 vuv left right False = intersectFM_C0 combiner fm1 split_key elt2 vuv 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 xyv xyw xyx = intersectFM_C2 xyv xyw xyx

intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 xyz xzu xzv = intersectFM_C3 xyz xzu xzv

The following Function with conditions
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt vvz 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 vvz fm_l fm_r) split_key = splitLT3 (Branch key elt vvz fm_l fm_r) split_key

splitLT0 key elt vvz fm_l fm_r split_key True = fm_l

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

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

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

splitLT4 EmptyFM split_key = emptyFM
splitLT4 xzy xzz = splitLT3 xzy xzz

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 vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
 | otherwise
 = mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)
where 
size_l  = sizeFM (Branch vxz vyu vyv vyw vyx)
size_r  = sizeFM (Branch vyz vzu vzv vzw vzx)

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 vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = 
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)
mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch0 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx otherwise
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch vxz vyu vyv vyw vyx)
size_r  = sizeFM (Branch vyz vzu vzv vzw vzx)

mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 yux yuy yuz yvu = mkVBalBranch3 yux yuy yuz yvu

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 yvw yvx yvy yvz = mkVBalBranch4 yvw yvx yvy yvz

The following Function with conditions
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt wuw 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 wuw fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuw fm_l fm_r) key_to_find

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

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

lookupFM0 key elt wuw fm_l fm_r key_to_find True = Just elt

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

lookupFM4 EmptyFM key = Nothing
lookupFM4 yww ywx = lookupFM3 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

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

is transformed to
gcd' x 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 :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a)

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

  addToFM :: Ord 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 xxv xxw xxx xxy = addToFM_C3 xxv xxw xxx xxy

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt vxw fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vxx 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 wux EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuy 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 vzy vzz EmptyFM) = (key,elt)
findMax (Branch key elt wuu wuv fm_r) = findMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt vwu EmptyFM vwv) = (key,elt)
findMin (Branch key elt vww fm_l vwx) = findMin fm_l

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

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

  foldFM :: (b  ->  c  ->  a  ->  a)  ->  a  ->  FiniteMap b c  ->  a
foldFM k z EmptyFM = z
foldFM k z (Branch key elt vvy 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 (zx,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (zy,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,zz) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,vuu) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xwu xwv = glueBal2 xwu xwv

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xwx xwy = glueBal3 xwx xwy

  glueVBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

  
glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = 
glueVBal2 vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * size_l < size_r) where 
glueVBal0 vy vz wu wv ww wy wz xu xv xw True = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)
glueVBal1 vy vz wu wv ww wy wz xu xv xw True = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
glueVBal1 vy vz wu wv ww wy wz xu xv xw False = glueVBal0 vy vz wu wv ww wy wz xu xv xw otherwise
glueVBal2 vy vz wu wv ww wy wz xu xv xw True = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
glueVBal2 vy vz wu wv ww wy wz xu xv xw False = glueVBal1 vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * size_r < size_l)
size_l = sizeFM (Branch vy vz wu wv ww)
size_r = sizeFM (Branch wy wz xu xv xw)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xuy xuz = glueVBal3 xuy xuz

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvv xvw = glueVBal4 xvv xvw

  intersectFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

  intersectFM_C :: Ord d => (c  ->  b  ->  a)  ->  FiniteMap d c  ->  FiniteMap d b  ->  FiniteMap d a
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 vuv left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right) = 
intersectFM_C1 combiner fm1 split_key elt2 vuv 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 vuv left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 vuv 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 vuv left right False = intersectFM_C0 combiner fm1 split_key elt2 vuv 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 xyv xyw xyx = intersectFM_C2 xyv xyw xyx

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 xyz xzu xzv = intersectFM_C3 xyz xzu xzv

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

  
lookupFM0 key elt wuw fm_l fm_r key_to_find True = Just elt

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

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

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

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yww ywx = lookupFM3 yww ywx

  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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr)
mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yu yv yw 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 zw 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 xx 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 vuw vux vuy vuz) = 
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 vvu vvv vvw vvx) = 
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 = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

  
mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = 
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * size_l < size_r) where 
mkVBalBranch0 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)
mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch0 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx otherwise
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * size_r < size_l)
size_l = sizeFM (Branch vxz vyu vyv vyw vyx)
size_r = sizeFM (Branch vyz vzu vzv vzw vzx)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 yux yuy yuz yvu = mkVBalBranch3 yux yuy yuz yvu

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 yvw yvx yvy yvz = mkVBalBranch4 yvw yvx yvy yvz

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch vwy vwz size vxu vxv) = size

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

  
splitGT0 key elt vw fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wzz xuu = splitGT3 wzz xuu

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

  
splitLT0 key elt vvz fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 xzy xzz = splitLT3 xzy xzz

  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



Let/Where Reductions:
The bindings of the following Let/Where expression
intersectFM_C1 combiner fm1 split_key elt2 vuv 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 vuv left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 vuv 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 vuv left right False = intersectFM_C0 combiner fm1 split_key elt2 vuv 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_C2Gts yzw yzx = splitGT yzw yzx

intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 vuv 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 vuv left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 vuv left right otherwise

intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

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

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 (zx,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (zy,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,zz) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,vuu) = mid_key2
vv2  = findMax fm1
vv3  = findMin fm2

are unpacked to the following functions on top level
glueBal2Mid_elt10 yzy yzz (zx,mid_elt1) = mid_elt1

glueBal2Vv3 yzy yzz = findMin yzy

glueBal2Mid_elt20 yzy yzz (zy,mid_elt2) = mid_elt2

glueBal2Mid_key20 yzy yzz (mid_key2,vuu) = mid_key2

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

glueBal2Mid_key10 yzy yzz (mid_key1,zz) = mid_key1

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

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

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

glueBal2Vv2 yzy yzz = findMax yzz

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

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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr)
mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R yz zu zv fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R yz zu zv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yu yv yw fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yu yv yw 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 zw 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 xx 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 yx (Branch key_rl elt_rl yy 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)

mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

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

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)

mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr otherwise

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 zw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zuu zuv fm_l fm_rl) fm_rr

mkBalBranch6Double_R zuu zuv zuw zux (Branch key_l elt_l xy fm_ll (Branch key_lr elt_lr xz 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)

mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux 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

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

mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr otherwise

mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr)

mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr)

The bindings of the following Let/Where expression
glueVBal2 vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * size_l < size_r)
where 
glueVBal0 vy vz wu wv ww wy wz xu xv xw True = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)
glueVBal1 vy vz wu wv ww wy wz xu xv xw True = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
glueVBal1 vy vz wu wv ww wy wz xu xv xw False = glueVBal0 vy vz wu wv ww wy wz xu xv xw otherwise
glueVBal2 vy vz wu wv ww wy wz xu xv xw True = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
glueVBal2 vy vz wu wv ww wy wz xu xv xw False = glueVBal1 vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch vy vz wu wv ww)
size_r  = sizeFM (Branch wy wz xu xv xw)

are unpacked to the following functions on top level
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw otherwise

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

glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw (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 vy vz wu wv ww wy wz xu xv xw True = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

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

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 vuw vux vuy vuz) = 
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 vvu vvv vvw vvx) = 
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 vuw vux vuy vuz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchRight_size zww zwx zwy = sizeFM zww

mkBranchBalance_ok zww zwx zwy = True

mkBranchUnbox zww zwx zwy x = x

mkBranchLeft_size zww zwx zwy = sizeFM zwx

mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key vvu vvv vvw vvx) = key < mkBranchRight_ok0Smallest_right_key fm_r

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

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

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)) zxw zxv

The bindings of the following Let/Where expression
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)
mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch0 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx otherwise
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
mkVBalBranch2 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch1 key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch vxz vyu vyv vyw vyx)
size_r  = sizeFM (Branch vyz vzu vzv vzw vzx)

are unpacked to the following functions on top level
mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx otherwise

mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (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 zyw zyx zyy zyz zzu)

mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

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

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

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'0 x y = gcd0Gcd' y (x `rem` y)

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

gcd0Gcd'1 True x ywy = x
gcd0Gcd'1 ywz yxu yxv = gcd0Gcd'0 yxu yxv

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



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

mainModule FiniteMap
  ((intersectFM :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a) :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char 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 = 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 xxv xxw xxx xxy = addToFM_C3 xxv xxw xxx xxy

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt vxw fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vxx 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 wux EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuy 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 vzy vzz EmptyFM) = (key,elt)
findMax (Branch key elt wuu wuv fm_r) = findMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt vwu EmptyFM vwv) = (key,elt)
findMin (Branch key elt vww fm_l vwx) = findMin fm_l

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

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

  foldFM :: (a  ->  c  ->  b  ->  b)  ->  b  ->  FiniteMap a c  ->  b
foldFM k z EmptyFM = z
foldFM k z (Branch key elt vvy 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 fm2 fm1 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 (zx,mid_elt1) = mid_elt1

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

  
glueBal2Mid_elt20 yzy yzz (zy,mid_elt2) = mid_elt2

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

  
glueBal2Mid_key10 yzy yzz (mid_key1,zz) = mid_key1

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

  
glueBal2Mid_key20 yzy yzz (mid_key2,vuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzz

  
glueBal2Vv3 yzy yzz = findMin yzy

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xwu xwv = glueBal2 xwu xwv

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xwx xwy = glueBal3 xwx xwy

  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 vy vz wu wv ww) (Branch wy wz xu xv xw) = glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

  
glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = glueVBal3GlueVBal2 vy vz wu wv ww wy wz xu xv xw vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * glueVBal3Size_l vy vz wu wv ww wy wz xu xv xw < glueVBal3Size_r vy vz wu wv ww wy wz xu xv xw)

  
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

  
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw otherwise

  
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw (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 xuy xuz = glueVBal3 xuy xuz

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvv xvw = glueVBal4 xvv xvw

  intersectFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

  intersectFM_C :: Ord c => (a  ->  b  ->  d)  ->  FiniteMap c a  ->  FiniteMap c b  ->  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 vuv left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 vuv 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 vuv 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 vuv 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 vuv left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 vuv 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 xyv xyw xyx = intersectFM_C2 xyv xyw xyx

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 xyz xzu xzv = intersectFM_C3 xyz xzu xzv

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

  
lookupFM0 key elt wuw fm_l fm_r key_to_find True = Just elt

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

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

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

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yww ywx = lookupFM3 yww ywx

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

  
mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw 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 zw 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 xx 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_r fm_l

  
mkBranchBalance_ok zww zwx zwy = True

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

  
mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vuw vux vuy vuz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zwx

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

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

  
mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key vvu vvv vvw vvx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zww

  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 vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

  
mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = mkVBalBranch3MkVBalBranch2 vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * mkVBalBranch3Size_l vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx < mkVBalBranch3Size_r vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx)

  
mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBranch 13 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

  
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx otherwise

  
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (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 zxx zxy zxz zyu zyv)

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

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 yux yuy yuz yvu = mkVBalBranch3 yux yuy yuz yvu

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 yvw yvx yvy yvz = mkVBalBranch4 yvw yvx yvy yvz

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch vwy vwz size vxu vxv) = size

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

  
splitGT0 key elt vw fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wzz xuu = splitGT3 wzz xuu

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

  
splitLT0 key elt vvz fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 xzy xzz = splitLT3 xzy xzz

  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 :: FiniteMap Char a  ->  FiniteMap Char a  ->  FiniteMap Char a)

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

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

  
addToFM0 old new = new

  addToFM_C :: Ord 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 xxv xxw xxx xxy = addToFM_C3 xxv xxw xxx xxy

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt vxw fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vxx 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 wux EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuy 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 vzy vzz EmptyFM) = (key,elt)
findMax (Branch key elt wuu wuv fm_r) = findMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt vwu EmptyFM vwv) = (key,elt)
findMin (Branch key elt vww fm_l vwx) = findMin fm_l

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

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

  foldFM :: (a  ->  c  ->  b  ->  b)  ->  b  ->  FiniteMap a c  ->  b
foldFM k z EmptyFM = z
foldFM k z (Branch key elt vvy 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 = glueBal4 EmptyFM fm2
glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM
glueBal fm1 fm2 = glueBal2 fm1 fm2

  
glueBal2 fm1 fm2 = glueBal2GlueBal1 fm2 fm1 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 (zx,mid_elt1) = mid_elt1

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

  
glueBal2Mid_elt20 yzy yzz (zy,mid_elt2) = mid_elt2

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

  
glueBal2Mid_key10 yzy yzz (mid_key1,zz) = mid_key1

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

  
glueBal2Mid_key20 yzy yzz (mid_key2,vuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzz

  
glueBal2Vv3 yzy yzz = findMin yzy

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xwu xwv = glueBal2 xwu xwv

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xwx xwy = glueBal3 xwx xwy

  glueVBal :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2
glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM
glueVBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

  
glueVBal3 (Branch vy vz wu wv ww) (Branch wy wz xu xv xw) = glueVBal3GlueVBal2 vy vz wu wv ww wy wz xu xv xw vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * glueVBal3Size_l vy vz wu wv ww wy wz xu xv xw < glueVBal3Size_r vy vz wu wv ww wy wz xu xv xw)

  
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = glueBal (Branch vy vz wu wv ww) (Branch wy wz xu xv xw)

  
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = mkBalBranch vy vz wv (glueVBal ww (Branch wy wz xu xv xw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw otherwise

  
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw True = mkBalBranch wy wz (glueVBal (Branch vy vz wu wv ww) xv) xw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv vy vz wu wv ww wy wz xu xv xw (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 xuy xuz = glueVBal3 xuy xuz

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvv xvw = glueVBal4 xvv xvw

  intersectFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2

  
intersectFM0 left right = right

  intersectFM_C :: Ord a => (c  ->  b  ->  d)  ->  FiniteMap a c  ->  FiniteMap a b  ->  FiniteMap a 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 vuv left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 vuv left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 vuv 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 vuv 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 vuv 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 vuv left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 vuv 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 xyv xyw xyx = intersectFM_C2 xyv xyw xyx

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 xyz xzu xzv = intersectFM_C3 xyz xzu xzv

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

  
lookupFM0 key elt wuw fm_l fm_r key_to_find True = Just elt

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

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

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

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yww ywx = lookupFM3 yww ywx

  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 yx (Branch key_rl elt_rl yy 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 xy fm_ll (Branch key_lr elt_lr xz 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 yz zu zv fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch yz zu zv fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R yz zu zv fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R yu yv yw fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch yu yv yw fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R yu yv yw 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 zw 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 xx 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_r fm_l

  
mkBranchBalance_ok zww zwx zwy = True

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

  
mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vuw vux vuy vuz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zwx

  
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)) zxw zxv

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

  
mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key vvu vvv vvw vvx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zww

  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 vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

  
mkVBalBranch3 key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx) = mkVBalBranch3MkVBalBranch2 vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * mkVBalBranch3Size_l vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx < mkVBalBranch3Size_r vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx)

  
mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vxz vyu vyv vyw vyx) (Branch vyz vzu vzv vzw vzx)

  
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vxz vyu vyw (mkVBalBranch key elt vyx (Branch vyz vzu vzv vzw vzx))
mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx otherwise

  
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx True = mkBalBranch vyz vzu (mkVBalBranch key elt (Branch vxz vyu vyv vyw vyx) vzw) vzx
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (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 zxx zxy zxz zyu zyv)

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

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 yux yuy yuz yvu = mkVBalBranch3 yux yuy yuz yvu

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 yvw yvx yvy yvz = mkVBalBranch4 yvw yvx yvy yvz

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

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = Pos Zero
sizeFM (Branch vwy vwz size vxu vxv) = size

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

  
splitGT0 key elt vw fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wzz xuu = splitGT3 wzz xuu

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

  
splitLT0 key elt vvz fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 xzy xzz = splitLT3 xzy xzz

  unitFM :: a  ->  b  ->  FiniteMap a b
unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  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

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

new_glueBal2Mid_key10(zzz2742, zzz2743, zzz2744, zzz2745, zzz2746, zzz2747, zzz2748, zzz2749, zzz2750, zzz2751, zzz2752, zzz2753, zzz2754, zzz2755, Branch(zzz27560, zzz27561, zzz27562, zzz27563, zzz27564), h, ba) → new_glueBal2Mid_key10(zzz2742, zzz2743, zzz2744, zzz2745, zzz2746, zzz2747, zzz2748, zzz2749, zzz2750, zzz2751, zzz27560, zzz27561, zzz27562, zzz27563, zzz27564, 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

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

new_glueBal2Mid_elt10(zzz2724, zzz2725, zzz2726, zzz2727, zzz2728, zzz2729, zzz2730, zzz2731, zzz2732, zzz2733, zzz2734, zzz2735, zzz2736, zzz2737, Branch(zzz27380, zzz27381, zzz27382, zzz27383, zzz27384), h, ba) → new_glueBal2Mid_elt10(zzz2724, zzz2725, zzz2726, zzz2727, zzz2728, zzz2729, zzz2730, zzz2731, zzz2732, zzz2733, zzz27380, zzz27381, zzz27382, zzz27383, zzz27384, 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

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

new_glueBal2Mid_key20(zzz2708, zzz2709, zzz2710, zzz2711, zzz2712, zzz2713, zzz2714, zzz2715, zzz2716, zzz2717, zzz2718, zzz2719, zzz2720, Branch(zzz27210, zzz27211, zzz27212, zzz27213, zzz27214), zzz2722, h, ba) → new_glueBal2Mid_key20(zzz2708, zzz2709, zzz2710, zzz2711, zzz2712, zzz2713, zzz2714, zzz2715, zzz2716, zzz2717, zzz27210, zzz27211, zzz27212, zzz27213, zzz27214, 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

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

new_glueBal2Mid_elt20(zzz2692, zzz2693, zzz2694, zzz2695, zzz2696, zzz2697, zzz2698, zzz2699, zzz2700, zzz2701, zzz2702, zzz2703, zzz2704, Branch(zzz27050, zzz27051, zzz27052, zzz27053, zzz27054), zzz2706, h, ba) → new_glueBal2Mid_elt20(zzz2692, zzz2693, zzz2694, zzz2695, zzz2696, zzz2697, zzz2698, zzz2699, zzz2700, zzz2701, zzz27050, zzz27051, zzz27052, zzz27053, zzz27054, 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

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

new_primMinusNat(Succ(zzz232400), Succ(zzz231800)) → new_primMinusNat(zzz232400, zzz231800)

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

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

new_primPlusNat(Succ(zzz7000), Succ(zzz620)) → new_primPlusNat(zzz7000, zzz620)

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

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

new_mkBalBranch6MkBalBranch11(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Succ(zzz281700), h, ba) → new_mkBalBranch6MkBalBranch11(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2809000, zzz281700, 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
                                  ↳ 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_mkBalBranch6MkBalBranch3(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Succ(zzz279500), h, ba) → new_mkBalBranch6MkBalBranch3(zzz231430, zzz231431, zzz2637, zzz231434, zzz2791000, zzz279500, 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
                                  ↳ 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_mkBalBranch6MkBalBranch01(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Succ(zzz280700), h, ba) → new_mkBalBranch6MkBalBranch01(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz2793000, zzz280700, 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
                                  ↳ 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_mkBalBranch6MkBalBranch4(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Succ(zzz278300), h, ba) → new_mkBalBranch6MkBalBranch4(zzz231430, zzz231431, zzz2637, zzz231434, zzz2739000, zzz278300, 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
                                  ↳ 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_deleteMax(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), h, ba) → new_deleteMax(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, 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
                                  ↳ 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_deleteMin(zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, h, ba) → new_deleteMin(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, 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
                                  ↳ 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_glueBal2GlueBal1(zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, Succ(zzz2596000), Succ(zzz2595000), h, ba) → new_glueBal2GlueBal1(zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2596000, zzz2595000, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Zero, h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz25470, h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz253000)), Pos(Succ(Succ(zzz2509000))), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Succ(zzz2509000), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz253700, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, Zero, h, ba)
new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Neg(zzz25270), zzz2509, h, ba) → new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25270), zzz2509, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Neg(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253700, zzz25470, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(zzz2509000), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25300), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Succ(Succ(zzz2509000)), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(zzz2537000), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253700), zzz25470, h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253700, zzz25470, h, ba)
new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Succ(zzz2509000))), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal16(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253700, Zero, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz253000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Succ(zzz2537000))), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25300), Neg(zzz25090), h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz25310, h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz250900, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25310), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Neg(zzz25430), zzz2537, h, ba) → new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25430), zzz2537, h, ba)
new_glueVBal3GlueVBal16(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(Succ(zzz2537000)), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, Succ(zzz25310), Pos(zzz25090), h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Succ(Zero), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz254600)), Pos(Succ(Succ(zzz2537000))), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz250900), zzz25310, h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, zzz25310, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Pos(zzz25370), h, ba) → new_glueVBal3(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz2537, h, ba) → new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), zzz2537, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25310), Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, zzz25310, h, ba)
new_glueVBal3GlueVBal16(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz254600), Succ(Succ(zzz2537000)), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(Succ(zzz2509000)), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz254600), Succ(zzz2537000), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz2509, h, ba) → new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), zzz2509, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Pos(zzz25270), zzz2509, h, ba) → new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25270), zzz2509, h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz25300, Zero, h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Pos(zzz25430), zzz2537, h, ba) → new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25430), zzz2537, h, ba)
new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)

The TRS R consists of the following rules:

new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primMulNat(Zero) → Zero
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primPlusNat3 → Zero
new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_sizeFM(Branch(zzz231430, zzz231431, zzz231432, zzz231433, zzz231434), h, ba)
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_sizeFM(Branch(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104), h, ba)
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bb, bc) → zzz21912
new_primPlusNat1(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 9 less nodes.

↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(zzz2537000), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Succ(zzz2509000))), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Zero, h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz25470, h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz253000)), Pos(Succ(Succ(zzz2509000))), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Succ(zzz2509000), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz253700, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz253000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Succ(zzz2537000))), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25300), Neg(zzz25090), h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)
new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz25310, h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz250900, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, Zero, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Neg(zzz25270), zzz2509, h, ba) → new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25270), zzz2509, h, ba)
new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25310), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, Succ(zzz25310), Pos(zzz25090), h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Neg(zzz25430), zzz2537, h, ba) → new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25430), zzz2537, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz254600)), Pos(Succ(Succ(zzz2537000))), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Neg(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253700, zzz25470, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Pos(zzz25370), h, ba) → new_glueVBal3(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25310), Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, zzz25310, h, ba)
new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz2537, h, ba) → new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), zzz2537, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(zzz2509000), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25300), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz254600), Succ(zzz2537000), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz2509, h, ba) → new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), zzz2509, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Pos(zzz25270), zzz2509, h, ba) → new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25270), zzz2509, h, ba)
new_glueVBal3(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz25300, Zero, h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Pos(zzz25430), zzz2537, h, ba) → new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25430), zzz2537, h, ba)
new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)

The TRS R consists of the following rules:

new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primMulNat(Zero) → Zero
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primPlusNat3 → Zero
new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_sizeFM(Branch(zzz231430, zzz231431, zzz231432, zzz231433, zzz231434), h, ba)
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_sizeFM(Branch(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104), h, ba)
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bb, bc) → zzz21912
new_primPlusNat1(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(zzz2537000), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Succ(zzz2509000))), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Zero, h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz25470, h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz253000)), Pos(Succ(Succ(zzz2509000))), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz253000), Succ(zzz2509000), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253000, zzz2509000, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal15(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz253700, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz253000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Zero), Pos(Succ(Succ(zzz2537000))), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25300), Neg(zzz25090), h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)
new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz25310, h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal26(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, zzz250900, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, Zero, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Neg(zzz25270), zzz2509, h, ba) → new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25270), zzz2509, h, ba)
new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25310), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, Branch(zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334), zzz231434, Succ(zzz25310), Pos(zzz25090), h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Neg(zzz25430), zzz2537, h, ba) → new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25430), zzz2537, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(Succ(zzz254600)), Pos(Succ(Succ(zzz2537000))), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Neg(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz253700, zzz25470, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, Branch(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044), zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25470), Pos(zzz25370), h, ba) → new_glueVBal3(zzz231040, zzz231041, zzz231042, zzz231043, zzz231044, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal21(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25310), Neg(Succ(zzz250900)), h, ba) → new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz250900, zzz25310, h, ba)
new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz2537, h, ba) → new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), zzz2537, h, ba)
new_glueVBal3GlueVBal22(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Succ(zzz2509000), h, ba) → new_glueVBal3GlueVBal24(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz25300), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Succ(zzz254600), Succ(zzz2537000), h, ba) → new_glueVBal3GlueVBal13(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz254600, zzz2537000, h, ba)
new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz2509, h, ba) → new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), zzz2509, h, ba)
new_glueVBal3GlueVBal12(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Succ(zzz253700)), h, ba) → new_glueVBal3GlueVBal14(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal2(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Pos(zzz25270), zzz2509, h, ba) → new_glueVBal3GlueVBal20(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25270), zzz2509, h, ba)
new_glueVBal3(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba) → new_glueVBal3GlueVBal29(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz2314330, zzz2314331, zzz2314332, zzz2314333, zzz2314334, h, ba), h, ba)
new_glueVBal3GlueVBal28(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, zzz25300, Zero, h, ba) → new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba)
new_glueVBal3GlueVBal10(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, Pos(zzz25430), zzz2537, h, ba) → new_glueVBal3GlueVBal11(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_primMulNat(zzz25430), zzz2537, h, ba)
new_glueVBal3GlueVBal23(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_glueVBal3GlueVBal1(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_sizeFM(Branch(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104), h, ba)
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bb, bc) → zzz21912
new_glueVBal3Size_r(zzz23100, zzz23101, zzz23102, zzz23103, zzz23104, zzz231430, zzz231431, zzz231432, zzz231433, zzz231434, h, ba) → new_sizeFM(Branch(zzz231430, zzz231431, zzz231432, zzz231433, zzz231434), h, ba)
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_splitLT2(zzz404, zzz405, zzz406, Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, h) → new_splitLT2(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, h)

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

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

new_addToFM_C2(Char(Succ(zzz7000)), zzz71, zzz72, zzz73, zzz74, zzz54, h) → new_addToFM_C(zzz73, zzz54, h)
new_addToFM_C(Branch(zzz730, zzz731, zzz732, zzz733, zzz734), zzz54, h) → new_addToFM_C2(zzz730, zzz731, zzz732, zzz733, zzz734, zzz54, h)

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
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Zero, ba) → new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), ba)
new_mkVBalBranch3(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, h) → new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, h)
new_mkVBalBranch3MkVBalBranch27(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Zero, bc) → new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), bc)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch16(zzz80, zzz81, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch25(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, ba) → new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), ba)
new_mkVBalBranch3MkVBalBranch24(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Succ(zzz7200), zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Succ(zzz16430), bc) → new_mkVBalBranch(zzz1641, zzz1631, zzz1632, Neg(Succ(zzz1633)), zzz1634, zzz1635, zzz1639, bc)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), h)
new_mkVBalBranch0(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, ba) → new_mkVBalBranch3MkVBalBranch13(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz1619), ba)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Pos(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), h)
new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8540), h) → new_mkVBalBranch3MkVBalBranch14(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8540, zzz7200), h)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch1(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch23(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch18(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Succ(zzz26900), bd) → new_mkVBalBranch0(zzz2688, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, bd)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1140), h) → new_mkVBalBranch3MkVBalBranch26(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, Succ(new_primPlusNat1(zzz1140, zzz8200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch24(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, Zero, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch10(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), ba) → new_mkVBalBranch3MkVBalBranch13(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), Succ(zzz1619), ba)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz8200, zzz7200, h)
new_mkVBalBranch3MkVBalBranch28(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch26(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, zzz8200, h)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch1(zzz80, zzz81, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz7980), h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz16290), ba) → new_mkVBalBranch(zzz1627, zzz1617, zzz1618, Pos(Succ(zzz1619)), zzz1620, zzz1621, zzz1625, ba)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8350), h) → new_mkVBalBranch3MkVBalBranch19(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8350, zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Succ(zzz16430), bc) → new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, zzz16420, zzz16430, bc)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch29(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, bc) → new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), bc)
new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, bc) → new_mkVBalBranch3MkVBalBranch18(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Zero, bc)
new_mkVBalBranch3MkVBalBranch110(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1140), h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch25(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, ba)
new_mkVBalBranch3MkVBalBranch18(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Succ(zzz26900), bd) → new_mkVBalBranch3MkVBalBranch18(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, zzz26890, zzz26900, bd)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch23(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch15(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz3120, zzz3121, zzz3122, zzz3123, zzz3124), h) → new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, h)
new_mkVBalBranch3MkVBalBranch13(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Succ(zzz26760), bb) → new_mkVBalBranch3MkVBalBranch13(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, zzz26750, zzz26760, bb)
new_mkVBalBranch3MkVBalBranch13(zzz2664, zzz2665, zzz2666, zzz2667, Branch(zzz26680, zzz26681, zzz26682, zzz26683, zzz26684), zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Succ(zzz26760), bb) → new_mkVBalBranch3(zzz2674, zzz26680, zzz26681, zzz26682, zzz26683, zzz26684, zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, bb)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Succ(zzz1140), h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch29(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, bc)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch24(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch14(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1051, h) → new_mkVBalBranch3MkVBalBranch15(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Succ(zzz16290), ba) → new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, zzz16280, zzz16290, ba)
new_mkVBalBranch3MkVBalBranch1(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch16(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch19(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1052, h) → new_mkVBalBranch3MkVBalBranch110(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz17250), bc) → new_mkVBalBranch3MkVBalBranch18(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Succ(zzz17250), bc)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3MkVBalBranch22(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(new_primPlusNat1(zzz1130, zzz8200)), zzz7200, h)

The TRS R consists of the following rules:

new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primPlusNat3 → Zero
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat1(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Zero, ba) → new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), ba)
new_mkVBalBranch3(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, h) → new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, h)
new_mkVBalBranch3MkVBalBranch27(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Zero, bc) → new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), bc)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch16(zzz80, zzz81, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch25(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, ba) → new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), ba)
new_mkVBalBranch3MkVBalBranch24(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Succ(zzz7200), zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Succ(zzz16430), bc) → new_mkVBalBranch(zzz1641, zzz1631, zzz1632, Neg(Succ(zzz1633)), zzz1634, zzz1635, zzz1639, bc)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), h)
new_mkVBalBranch0(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, ba) → new_mkVBalBranch3MkVBalBranch13(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz1619), ba)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Pos(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), h)
new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8540), h) → new_mkVBalBranch3MkVBalBranch14(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8540, zzz7200), h)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch1(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch23(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch18(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Succ(zzz26900), bd) → new_mkVBalBranch0(zzz2688, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, bd)
new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1140), h) → new_mkVBalBranch3MkVBalBranch26(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, Succ(new_primPlusNat1(zzz1140, zzz8200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, Zero, zzz73, zzz74, zzz55, h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch3MkVBalBranch10(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch12(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), ba) → new_mkVBalBranch3MkVBalBranch13(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), Succ(zzz1619), ba)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz8200, zzz7200, h)
new_mkVBalBranch3MkVBalBranch28(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch26(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, zzz8200, h)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch1(zzz80, zzz81, zzz83, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz7980), h) → new_mkVBalBranch3(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3MkVBalBranch11(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), h)
new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz16290), ba) → new_mkVBalBranch(zzz1627, zzz1617, zzz1618, Pos(Succ(zzz1619)), zzz1620, zzz1621, zzz1625, ba)
new_mkVBalBranch3MkVBalBranch10(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8350), h) → new_mkVBalBranch3MkVBalBranch19(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8350, zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Succ(zzz16430), bc) → new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, zzz16420, zzz16430, bc)
new_mkVBalBranch3MkVBalBranch29(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, bc) → new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), bc)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch2(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch110(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1140), h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch25(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, ba)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch23(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch18(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Succ(zzz26900), bd) → new_mkVBalBranch3MkVBalBranch18(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, zzz26890, zzz26900, bd)
new_mkVBalBranch3MkVBalBranch15(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h) → new_mkVBalBranch0(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, h)
new_mkVBalBranch(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz3120, zzz3121, zzz3122, zzz3123, zzz3124), h) → new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, h)
new_mkVBalBranch3MkVBalBranch13(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Succ(zzz26760), bb) → new_mkVBalBranch3MkVBalBranch13(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, zzz26750, zzz26760, bb)
new_mkVBalBranch3MkVBalBranch13(zzz2664, zzz2665, zzz2666, zzz2667, Branch(zzz26680, zzz26681, zzz26682, zzz26683, zzz26684), zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Succ(zzz26760), bb) → new_mkVBalBranch3(zzz2674, zzz26680, zzz26681, zzz26682, zzz26683, zzz26684, zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, bb)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Succ(zzz1140), h) → new_mkVBalBranch(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, h)
new_mkVBalBranch3MkVBalBranch26(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch29(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, bc)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch24(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch14(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1051, h) → new_mkVBalBranch3MkVBalBranch15(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Succ(zzz16290), ba) → new_mkVBalBranch3MkVBalBranch22(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, zzz16280, zzz16290, ba)
new_mkVBalBranch3MkVBalBranch1(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch16(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch19(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1052, h) → new_mkVBalBranch3MkVBalBranch110(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch21(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, h)
new_mkVBalBranch3MkVBalBranch17(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz17250), bc) → new_mkVBalBranch3MkVBalBranch18(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Succ(zzz17250), bc)
new_mkVBalBranch3MkVBalBranch20(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), h) → new_mkVBalBranch3MkVBalBranch22(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(new_primPlusNat1(zzz1130, zzz8200)), zzz7200, h)

The TRS R consists of the following rules:

new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primPlusNat3 → Zero
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat1(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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



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

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

new_addToFM_C1(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Zero, ba) → new_addToFM_C0(zzz2463, zzz2464, zzz2465, ba)
new_addToFM_C0(Branch(Char(Zero), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bb) → new_addToFM_C0(zzz344, zzz3000, zzz31, bb)
new_addToFM_C20(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Succ(zzz18400), h) → new_addToFM_C20(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, zzz18390, zzz18400, h)
new_addToFM_C21(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, h) → new_addToFM_C1(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz1837), Succ(zzz1832), h)
new_addToFM_C1(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Succ(zzz24670), ba) → new_addToFM_C1(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, zzz24660, zzz24670, ba)
new_addToFM_C20(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Succ(zzz18400), h) → new_addToFM_C0(zzz1835, zzz1837, zzz1838, h)
new_addToFM_C0(Branch(Char(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bb) → new_addToFM_C20(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bb)
new_addToFM_C20(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Zero, h) → new_addToFM_C1(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz1837), Succ(zzz1832), h)
new_addToFM_C20(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Zero, h) → new_addToFM_C21(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, h)

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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz254200), zzz25320, bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch119(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253900, Zero, ba)
new_mkVBalBranch3MkVBalBranch119(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(Succ(zzz2535000)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz253800), zzz25280, ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch129(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(Succ(zzz2540000)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch129(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254400, Zero, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch119(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(Succ(zzz2535000)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch129(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(Succ(zzz2540000)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primMulNat(Zero) → Zero
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_sizeFM(EmptyFM, bc, bd) → Pos(Zero)
new_primPlusNat3 → Zero
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primPlusNat1(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 8 less nodes.

↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primMulNat(Zero) → Zero
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_sizeFM(EmptyFM, bc, bd) → Pos(Zero)
new_primPlusNat3 → Zero
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primPlusNat1(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h) at position [12] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch213(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 6 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba) at position [13] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), h) at position [12] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch218(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 5 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, ba), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), ba) → new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch135(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Succ(zzz253800)), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch114(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch134(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 7 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb) at position [13] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, ba), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_primMulNat1(x0)



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

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, bb), bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), bb) → new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch125(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Pos(Succ(Succ(zzz2540000))), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch126(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), bb) → new_mkVBalBranch3MkVBalBranch130(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, bb)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch123(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 7 less nodes.

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, bb), bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2486)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch132(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), bc, bd) → zzz21912
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Zero, Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_sizeFM(EmptyFM, 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(Succ(Succ(new_primPlusNat0(zzz34200))), Succ(zzz34200)), h) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch136(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), ba) → new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), ba) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, ba) → new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch116(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), ba) → new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch133(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.

↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch113(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), ba) → new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(Succ(zzz2471)), ba) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch115(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Pos(Succ(Succ(zzz2535000))), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), bb) → new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), bb) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primMulNat(Succ(z7)), z12) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primMulNat(Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_primMulNat(Succ(x0))
new_primMulNat(Zero)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(new_primMulNat0(z7), Succ(z7)), z12) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primMulNat0(x0)
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_primMulNat0(x0)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, new_primPlusNat1(Succ(Succ(new_primPlusNat0(z7))), Succ(z7)), z12) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)



↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Instantiation
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz254200)), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, bb) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x3 + x4 + x5   
POL(Neg(x1)) = x1   
POL(Pos(x1)) = x1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch1(x1, x2, x3, x4, x5)) = x3   
POL(new_mkVBalBranch3MkVBalBranch111(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch112(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch113(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch115(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x1 + x5   
POL(new_mkVBalBranch3MkVBalBranch117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x1 + x3 + x5   
POL(new_mkVBalBranch3MkVBalBranch118(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch120(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x4   
POL(new_mkVBalBranch3MkVBalBranch121(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x4   
POL(new_mkVBalBranch3MkVBalBranch122(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch124(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch127(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x5   
POL(new_mkVBalBranch3MkVBalBranch128(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch131(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x5   
POL(new_mkVBalBranch3MkVBalBranch210(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch214(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x1 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch219(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x4 + x5   
POL(new_primPlusNat0(x1)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_primPlusNat2(x1)) = 0   
POL(new_primPlusNat3) = 0   
POL(new_primPlusNat4(x1)) = 0   
POL(new_primPlusNat5(x1)) = 0   
POL(new_primPlusNat6(x1)) = 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch120(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 3 SCCs with 2 less nodes.

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, h)

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)



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

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

new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, h)

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

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

new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Pos(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(zzz34200)), zzz34200))), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x2 + x3 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch1(x1, x2, x3, x4, x5)) = x3   
POL(new_mkVBalBranch3MkVBalBranch111(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch112(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x5   
POL(new_mkVBalBranch3MkVBalBranch113(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch115(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x5   
POL(new_mkVBalBranch3MkVBalBranch117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x5   
POL(new_mkVBalBranch3MkVBalBranch118(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch122(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch124(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch127(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x5   
POL(new_mkVBalBranch3MkVBalBranch128(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch131(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x5   
POL(new_mkVBalBranch3MkVBalBranch210(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch214(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x5   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch219(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_primPlusNat0(x1)) = 0   
POL(new_primPlusNat1(x1, x2)) = x1 + x2   
POL(new_primPlusNat2(x1)) = 1   
POL(new_primPlusNat3) = 1   
POL(new_primPlusNat4(x1)) = 1   
POL(new_primPlusNat5(x1)) = 1 + x1   
POL(new_primPlusNat6(x1)) = x1   

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

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

new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)
new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch1(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ba)
new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch118(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch111(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), h) → new_mkVBalBranch1(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, ba)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch115(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(z12), Pos(Succ(Succ(x13))), z13) → new_mkVBalBranch3MkVBalBranch117(z0, z1, Succ(x13), z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, x13, z13)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, ba) → new_mkVBalBranch3MkVBalBranch112(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz2476)), ba)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch113(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(y_1)), z12) → new_mkVBalBranch3MkVBalBranch115(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(y_1), Pos(Succ(z2)), z12)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 3 SCCs with 8 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), ba) → new_mkVBalBranch1(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, ba)
new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), h) → new_mkVBalBranch3MkVBalBranch211(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, h)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch210(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), ba) → new_mkVBalBranch3MkVBalBranch211(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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



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

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

new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), bb) → new_mkVBalBranch1(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x4   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch1(x1, x2, x3, x4, x5)) = x4   
POL(new_mkVBalBranch3MkVBalBranch122(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch124(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch127(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch128(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch131(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch219(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x9   
POL(new_primPlusNat0(x1)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_primPlusNat2(x1)) = 0   
POL(new_primPlusNat3) = 0   
POL(new_primPlusNat4(x1)) = 0   
POL(new_primPlusNat5(x1)) = 0   
POL(new_primPlusNat6(x1)) = 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ DependencyGraphProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ DependencyGraphProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ DependencyGraphProof
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ DependencyGraphProof
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ UsableRulesProof
                                                                                                          ↳ QDP
                                                                                                            ↳ QReductionProof
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ DependencyGraphProof
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QReductionProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ AND
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                  ↳ QDPOrderProof
                                                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                                                      ↳ DependencyGraphProof
                                                                                                                                                                                                                                                        ↳ AND
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ QDPOrderProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                          ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch3MkVBalBranch122(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz2491)), bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, bb)
new_mkVBalBranch3MkVBalBranch124(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), bb) → new_mkVBalBranch3MkVBalBranch131(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(Succ(zzz2486)), bb)
new_mkVBalBranch3MkVBalBranch131(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, Neg(Succ(z2)), z13) → new_mkVBalBranch3MkVBalBranch127(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z2, z12, z13)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch219(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), bb) → new_mkVBalBranch3MkVBalBranch216(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, bb)
new_mkVBalBranch3MkVBalBranch127(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), bb) → new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb)
new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), h) → new_mkVBalBranch3MkVBalBranch216(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), h)
new_mkVBalBranch3MkVBalBranch122(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z7)), z12) → new_mkVBalBranch3MkVBalBranch124(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat0(z7)), z7))), z12)
new_mkVBalBranch3MkVBalBranch128(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, bb) → new_mkVBalBranch1(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), bb)
new_mkVBalBranch1(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, Succ(Succ(new_primPlusNat0(zzz58200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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



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

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

new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat3 → Zero
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)

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

new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat3
new_primPlusNat6(Succ(x0))
new_primPlusNat0(Succ(x0))
new_primPlusNat1(Zero, Zero)
new_primPlusNat2(Zero)
new_primPlusNat6(Zero)
new_primPlusNat4(Succ(x0))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero)
new_primPlusNat4(Zero)
new_primPlusNat2(Succ(x0))
new_primPlusNat5(x0)



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

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

new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), ba) → new_mkVBalBranch3MkVBalBranch117(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, 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
                                  ↳ 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_splitGT2(zzz404, zzz405, zzz406, Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, h) → new_splitGT2(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, h)

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

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

new_splitLT(Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ba) → new_splitLT3(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ba)
new_splitLT21(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Succ(zzz13000), bb) → new_splitLT(zzz1296, zzz1298, bb)
new_splitLT20(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ba) → new_splitLT20(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ba)
new_splitLT21(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Succ(zzz13000), bb) → new_splitLT21(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, zzz12990, zzz13000, bb)
new_splitLT3(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ba) → new_splitLT20(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ba)
new_splitLT21(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Zero, bb) → new_splitLT22(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, bb)
new_splitLT1(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Zero, h) → new_splitLT(zzz2099, zzz2100, h)
new_splitLT20(Char(Succ(zzz57600)), zzz577, zzz578, zzz579, zzz580, zzz581, ba) → new_splitLT21(zzz57600, zzz577, zzz578, zzz579, zzz580, zzz581, zzz581, zzz57600, ba)
new_splitLT20(Char(Zero), zzz577, zzz578, EmptyFM, Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ba) → new_splitLT3(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ba)
new_splitLT1(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Succ(zzz21020), h) → new_splitLT1(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, zzz21010, zzz21020, h)
new_splitLT22(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, bb) → new_splitLT1(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz1298), Succ(zzz1293), bb)
new_splitLT21(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Zero, bb) → new_splitLT1(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz1298), Succ(zzz1293), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_splitGT20(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Succ(zzz15280), h) → new_splitGT1(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz1526), Succ(zzz1521), h)
new_splitGT1(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Succ(zzz17840), bb) → new_splitGT(zzz1780, zzz1782, bb)
new_splitGT(Branch(Char(Zero), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, ba) → new_splitGT22(zzz8241, zzz8242, zzz8243, zzz8244, zzz825, ba)
new_splitGT20(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Zero, h) → new_splitGT21(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, h)
new_splitGT20(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Zero, h) → new_splitGT(zzz1525, zzz1526, h)
new_splitGT21(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, h) → new_splitGT1(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz1526), Succ(zzz1521), h)
new_splitGT(Branch(Char(Succ(zzz824000)), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, ba) → new_splitGT20(zzz824000, zzz8241, zzz8242, zzz8243, zzz8244, zzz825, zzz825, zzz824000, ba)
new_splitGT22(zzz821, zzz822, zzz823, Branch(Char(Succ(zzz824000)), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, ba) → new_splitGT20(zzz824000, zzz8241, zzz8242, zzz8243, zzz8244, zzz825, zzz825, zzz824000, ba)
new_splitGT22(zzz821, zzz822, zzz823, Branch(Char(Zero), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, ba) → new_splitGT22(zzz8241, zzz8242, zzz8243, zzz8244, zzz825, ba)
new_splitGT1(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Succ(zzz17840), bb) → new_splitGT1(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, zzz17830, zzz17840, bb)
new_splitGT20(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Succ(zzz15280), h) → new_splitGT20(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, zzz15270, zzz15280, h)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof

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

new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT0(zzz3000, zzz31, zzz32, zzz34, bd), zzz43, bd)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Zero, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Succ(zzz16100), ca, cb) → new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, zzz16090, zzz16100, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, zzz10210, zzz10220, h, ba)
new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Zero, Zero, h, ba) → new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Zero, bg, bh) → new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Succ(zzz13440), bb, bc) → new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz13430, zzz13440, bb, bc)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, Branch(zzz4160, zzz4161, zzz4162, zzz4163, zzz4164), zzz417, cc, cd) → new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, zzz4160, zzz4161, zzz4162, zzz4163, zzz4164, cc, cd)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Zero, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Zero, ca, cb) → new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Zero, ca, cb) → new_intersectFM_C2IntersectFM_C18(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT23(Char(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Succ(zzz83000)), zzz831, zzz832, zzz833, zzz834, be, bf) → new_intersectFM_C2IntersectFM_C16(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz83000, zzz831, zzz832, zzz833, zzz834, zzz825, zzz83000, be, bf)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz11520, zzz11530, bg, bh)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C18(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1150, bg, bh)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Zero, bb, bc) → new_intersectFM_C2IntersectFM_C11(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1342, bb, bc)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_mkVBalBranch2(zzz3000, zzz31, new_splitGT4(bd), zzz34, bd), zzz44, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C15(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitGT0(zzz4000, bd), zzz44, bd)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Zero, bb, bc) → new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)

The TRS R consists of the following rules:

new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz2637, dc, dd)
new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1052, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb) → new_addToFM_C10(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz1837), Succ(zzz1832), eb)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, dg)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkVBalBranch5(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz26370, zzz26371, zzz26373, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz231430, zzz231431, zzz26374, zzz231434, dc, dd), dc, dd)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), db) → new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28240), dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28240, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBalBranch(zzz2484, zzz2485, zzz2487, new_mkVBalBranch2(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), dg), ty_Char, dg)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), dg) → new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Succ(zzz253500), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz253500, db)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, EmptyFM, dc, dd) → error([])
new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1051, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_addToFM_C4(Branch(zzz730, zzz731, zzz732, zzz733, zzz734), zzz54, bd) → new_addToFM_C22(zzz730, zzz731, zzz732, zzz733, zzz734, zzz54, bd)
new_splitLT0(zzz3000, zzz31, zzz32, zzz34, bd) → new_splitLT40(bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(new_primPlusNat1(zzz1130, zzz8200)), zzz7200, bd)
new_splitGT5(EmptyFM, cc) → new_splitGT4(cc)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Pos(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz25400, dg)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28010), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), db) → new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, db)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27850), dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27850, dc, dd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28220), zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28220, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), dg) → new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, dg)
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg), dg)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Zero, zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT24(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), dg) → new_mkBalBranch(zzz2489, zzz2490, new_mkVBalBranch2(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, dg), zzz2493, ty_Char, dg)
new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd) → new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, bd)
new_addToFM0(zzz34, zzz3000, zzz31, bd) → new_addToFM_C3(zzz34, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_addToFM_C3(EmptyFM, zzz3000, zzz31, bd) → Branch(Char(Succ(zzz3000)), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8350), bd) → new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8350, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd)
new_mkBranch(zzz2812, zzz2813, zzz2814, zzz2815, zzz2816, eg, eh) → Branch(zzz2813, zzz2814, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM(zzz2815, eg, eh)), new_sizeFM(zzz2816, eg, eh)), zzz2815, zzz2816)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz2793000, zzz280700, dc, dd)
new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Zero)), zzz2314340, zzz2314341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz231430, zzz231431, zzz2637, zzz2314343, dc, dd), zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz2791000, zzz279500, dc, dd)
new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Succ(zzz16430), df) → new_mkBalBranch(zzz1636, zzz1637, new_mkVBalBranch6(zzz1641, zzz1631, zzz1632, Neg(Succ(zzz1633)), zzz1634, zzz1635, zzz1639, df), zzz1640, ty_Char, df)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd) → zzz33
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, zzz582, zzz583, zzz584), EmptyFM, bd) → new_addToFM0(Branch(zzz580, zzz581, zzz582, zzz583, zzz584), zzz3000, zzz31, bd)
new_mkVBalBranch4(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, bd)
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, EmptyFM, zzz231434, dc, dd) → error([])
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2784, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27880), zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz27880, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28050), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, dg)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitLT5(Branch(Char(Zero), zzz821, zzz822, zzz823, zzz824), zzz825, be)
new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de) → new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), de)
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da) → Branch(Char(Succ(zzz2464)), new_addToFM00(zzz2460, zzz2465, da), zzz2461, zzz2462, zzz2463)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Succ(zzz17840), ea) → new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, zzz17830, zzz17840, ea)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Succ(zzz13000), dh) → new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, zzz12990, zzz13000, dh)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Zero, da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Succ(zzz28170), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz28170, dc, dd)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2821, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_splitGT4(bd) → new_emptyFM(bd)
new_mkVBalBranch7(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, bd)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Succ(zzz21020), ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, EmptyFM, zzz231434, dc, dd) → error([])
new_mkVBalBranch8(zzz2674, Branch(zzz26680, zzz26681, zzz26682, zzz26683, zzz26684), zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_mkVBalBranch30(zzz2674, zzz26680, zzz26681, zzz26682, zzz26683, zzz26684, zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, ec)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Succ(zzz16430), df) → new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, zzz16420, zzz16430, df)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Succ(zzz21020), ce) → new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, zzz21010, zzz21020, ce)
new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2494)), zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg)
new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2818, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_splitGT0(zzz4000, bd) → new_splitGT40(zzz4000, bd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_primPlusInt(Neg(zzz23240), Neg(zzz23180)) → Neg(new_primPlusNat1(zzz23240, zzz23180))
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28080), zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28080, zzz279300, dc, dd)
new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_mkVBalBranch2(zzz404, zzz405, new_splitGT5(zzz407, cc), zzz408, cc)
new_splitLT40(bd) → new_emptyFM(bd)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea) → zzz1781
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz266200)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be)
new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg) → new_splitGT10(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz1526), Succ(zzz1521), cg)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd) → new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd)
new_mkVBalBranch7(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch8(zzz2674, EmptyFM, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_addToFM(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), db) → new_mkBalBranch(zzz2474, zzz2475, new_mkVBalBranch2(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, db), zzz2478, ty_Char, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd) → new_addToFM_C4(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, bd)
new_splitLT41(zzz4000, bd) → new_emptyFM(bd)
new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz231434, dc, dd)
new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce) → zzz2098
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef), ef)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT5(EmptyFM, zzz581, ef) → new_splitLT41(zzz581, ef)
new_addToFM00(zzz71, zzz54, bd) → zzz54
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_splitLT5(Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, Branch(zzz23143430, zzz23143431, zzz23143432, zzz23143433, zzz23143434), zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz23143430, zzz23143431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz231430, zzz231431, zzz2637, zzz23143433, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz2314340, zzz2314341, zzz23143434, zzz2314344, dc, dd), dc, dd)
new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd) → new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Succ(zzz15280), cg) → new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, zzz15270, zzz15280, cg)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_primMinusNat0(Succ(zzz232400), Zero) → Pos(Succ(zzz232400))
new_sizeFM(EmptyFM, ed, ee) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Succ(zzz254000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz254000, dg)
new_primMulNat2(Succ(zzz279400)) → new_primPlusNat1(new_primPlusNat1(Zero, Succ(zzz279400)), Succ(zzz279400))
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Zero, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch7(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Neg(zzz25350), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2688, Branch(zzz2678, zzz2679, Neg(Succ(zzz2680)), zzz2681, zzz2682), Branch(zzz2683, zzz2684, Neg(Succ(zzz2685)), zzz2686, zzz2687), ty_Char, cf)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz253800), zzz25280, db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, db)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, bd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28030), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz28030, dc, dd)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz254200), zzz25320, dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, dg)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2799, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Succ(zzz26760), ec) → new_mkBalBranch(zzz2664, zzz2665, zzz2667, new_mkVBalBranch8(zzz2674, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec), ty_Char, ec)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), EmptyFM, zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT41(zzz581, ef), ef)
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz3120, zzz3121, zzz3122, zzz3123, zzz3124), bd) → new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27900), dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz27900, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253900, Zero, db)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), db) → new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz17250), df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Succ(zzz17250), df)
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2788, dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, zzz2788, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28230), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2796, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_primMulNat(Zero) → Zero
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT25(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, bd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBalBranch(zzz2469, zzz2470, zzz2472, new_mkVBalBranch2(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), db), ty_Char, db)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Succ(zzz17840), ea) → new_mkVBalBranch2(zzz1777, zzz1778, new_splitGT3(zzz1780, zzz1782, ea), zzz1781, ea)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_addToFM_C4(EmptyFM, zzz54, bd) → Branch(Char(Zero), zzz54, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_primPlusInt(Pos(zzz23240), Neg(zzz23180)) → new_primMinusNat0(zzz23240, zzz23180)
new_primPlusInt(Neg(zzz23240), Pos(zzz23180)) → new_primMinusNat0(zzz23180, zzz23240)
new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh) → new_splitLT10(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz1298), Succ(zzz1293), dh)
new_splitGT3(Branch(Char(Succ(zzz824000)), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT24(zzz824000, zzz8241, zzz8242, zzz8243, zzz8244, zzz825, zzz825, zzz824000, be)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_splitGT5(Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT23(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, EmptyFM, zzz2314344, dc, dd) → error([])
new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch5(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Succ(zzz28070), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, zzz28070, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), bd)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Zero, df)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8540), bd) → new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8540, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2800, dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, zzz2800, zzz279100, dc, dd)
new_addToFM_C22(Char(Succ(zzz7000)), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → new_mkBalBranch(Char(Succ(zzz7000)), zzz71, new_addToFM_C4(zzz73, zzz54, bd), zzz74, ty_Char, bd)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Succ(zzz18400), eb) → new_mkBalBranch(Char(Succ(zzz1832)), zzz1833, new_addToFM_C3(zzz1835, zzz1837, zzz1838, eb), zzz1836, ty_Char, eb)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, zzz8200, bd)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254400, Zero, dg)
new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitLT24(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_splitGT5(Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT26(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Succ(Zero), zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitLT5(Branch(Char(Succ(zzz1006)), zzz1007, zzz1008, zzz1009, zzz1010), zzz1011, h)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25420, zzz25320, dg)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Zero, cg) → new_splitGT3(zzz1525, zzz1526, cg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkVBalBranch2(zzz3000, zzz31, EmptyFM, zzz34, bd) → new_addToFM0(zzz34, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2674, Branch(zzz2664, zzz2665, Pos(Succ(zzz2666)), zzz2667, zzz2668), Branch(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673), ty_Char, ec)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Zero, ce) → new_mkVBalBranch2(zzz2095, zzz2096, zzz2098, new_splitLT5(zzz2099, zzz2100, ce), ce)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, new_primPlusInt(new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)), dc, dd)
new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Succ(zzz26620000)))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28190), dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz28190, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28060), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28060, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2822, dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2822, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), db) → new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz2739000, zzz278300, dc, dd)
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Succ(zzz7200), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_splitGT3(Branch(Char(Zero), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT27(zzz8241, zzz8242, zzz8243, zzz8244, zzz825, be)
new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd)
new_splitGT3(EmptyFM, zzz825, be) → new_splitGT40(zzz825, be)
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, Branch(zzz263740, zzz263741, zzz263742, zzz263743, zzz263744), zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz263740, zzz263741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz26370, zzz26371, zzz26373, zzz263743, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz231430, zzz231431, zzz263744, zzz231434, dc, dd), dc, dd)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Succ(zzz24670), da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, db)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz16290), de) → new_mkBalBranch(zzz1622, zzz1623, new_mkVBalBranch6(zzz1627, zzz1617, zzz1618, Pos(Succ(zzz1619)), zzz1620, zzz1621, zzz1625, de), zzz1626, ty_Char, de)
new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2479)), zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db)
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), ed, ee) → zzz21912
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Neg(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, EmptyFM, bd) → new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd)
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitGT24(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, Succ(zzz1011), Succ(zzz1006), h)
new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2787, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Zero, cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_primPlusInt(Pos(zzz23240), Pos(zzz23180)) → Pos(new_primPlusNat1(zzz23240, zzz23180))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Succ(zzz27950), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz27950, dc, dd)
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, Branch(zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344), dc, dd) → new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_sizeFM(zzz2314343, dc, dd), new_sizeFM(zzz2314344, dc, dd), dc, dd)
new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT3(zzz824, zzz825, be)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), db) → new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27890), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27970), dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27970, dc, dd)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Zero))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_emptyFM(bd) → EmptyFM
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz7980), bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27980), dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz8200, zzz7200, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Zero)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Zero, ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), dg) → new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28020), dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz28020, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, bd) → new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), bd)
new_addToFM_C22(Char(Zero), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → Branch(Char(Zero), new_addToFM00(zzz71, zzz54, bd), zzz72, zzz73, zzz74)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd) → zzz34
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_addToFM_C3(Branch(Char(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_addToFM_C23(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bd)
new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, Branch(zzz26370, zzz26371, zzz26372, zzz26373, zzz26374), zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_sizeFM(zzz26374, dc, dd), new_sizeFM(zzz26373, dc, dd), dc, dd)
new_primMinusNat0(Zero, Succ(zzz231800)) → Neg(Succ(zzz231800))
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Succ(zzz26900), cf) → new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, zzz26890, zzz26900, cf)
new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef) → new_splitLT23(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_mkVBalBranch4(zzz55, EmptyFM, zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_splitLT23(Char(Succ(zzz57600)), zzz577, zzz578, zzz579, zzz580, zzz581, ef) → new_splitLT27(zzz57600, zzz577, zzz578, zzz579, zzz580, zzz581, zzz581, zzz57600, ef)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Succ(zzz24670), da) → new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, zzz24660, zzz24670, da)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Succ(zzz16290), de) → new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, zzz16280, zzz16290, de)
new_mkVBalBranch5(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, bd)
new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT23(Char(Zero), zzz577, zzz578, EmptyFM, zzz580, zzz581, ef) → new_addToFM_C4(new_splitLT5(zzz580, zzz581, ef), zzz577, ef)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Succ(zzz26900), cf) → new_mkBalBranch(zzz2678, zzz2679, zzz2681, new_mkVBalBranch4(zzz2688, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, cf), ty_Char, cf)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2809000, zzz281700, dc, dd)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Zero, da) → new_mkBalBranch(Char(Succ(zzz2459)), zzz2460, zzz2462, new_addToFM_C3(zzz2463, zzz2464, zzz2465, da), ty_Char, da)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_primPlusNat1(Zero, Zero) → Zero
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28040), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_primPlusNat3 → Zero
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Succ(zzz26760), ec) → new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, zzz26750, zzz26760, ec)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27860), dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Succ(zzz15280), cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(zzz25350), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz25350, db)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28000), zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz28000, zzz279100, dc, dd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Succ(zzz18400), eb) → new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, zzz18390, zzz18400, eb)
new_splitLT24(zzz404, zzz405, zzz406, EmptyFM, zzz408, cc) → new_splitLT40(cc)
new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, Succ(new_primPlusNat1(zzz1140, zzz8200)), bd)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(zzz25380), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25380, zzz25280, db)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28200), dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_splitGT40(zzz4000, bd) → new_emptyFM(bd)
new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_addToFM_C3(Branch(Char(Zero), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_mkBalBranch(Char(Zero), zzz341, zzz343, new_addToFM_C3(zzz344, zzz3000, zzz31, bd), ty_Char, bd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), zzz279300, dc, dd)
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, db)
new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Succ(zzz13000), dh) → new_splitLT5(zzz1296, zzz1298, dh)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Succ(zzz27830), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz27830, dc, dd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, new_primMulNat2(zzz27940), dc, dd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df) → new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), df)
new_primMinusNat0(Succ(zzz232400), Succ(zzz231800)) → new_primMinusNat0(zzz232400, zzz231800)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT5(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5)
new_primMinusNat0(Zero, Zero)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch32(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch2(x0, x1, EmptyFM, x2, x3)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch32(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5)
new_addToFM_C3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6, x7)
new_splitGT5(EmptyFM, x0)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT26(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_splitLT30(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primPlusNat6(Succ(x0))
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_splitGT3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_splitLT23(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_primPlusNat5(x0)
new_addToFM_C22(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, x5)
new_addToFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_primMulNat(Zero)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT23(Char(Zero), x0, x1, EmptyFM, x2, x3, x4)
new_splitGT27(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_primPlusNat2(Zero)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_mkVBalBranch40(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch5(x0, EmptyFM, x1, x2, x3, x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch7(x0, EmptyFM, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch30(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5)
new_emptyFM(x0)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_primMinusNat0(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7)
new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5)
new_primPlusNat0(Succ(x0))
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_primPlusNat0(Zero)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch8(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, x12)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_splitGT40(x0, x1)
new_primPlusNat6(Zero)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Zero, x4, x5, x6)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch240(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT4(x0, x1, x2, x3, x4)
new_mkVBalBranch8(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, EmptyFM, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT0(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_primPlusNat4(Succ(x0))
new_addToFM0(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_splitLT26(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_splitLT24(x0, x1, x2, Branch(Char(Succ(x3)), x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitLT41(x0, x1)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_splitGT4(x0)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT25(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Succ(x10), x11)
new_splitGT3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT24(x0, x1, x2, Branch(Char(Zero), x3, x4, x5, x6), x7, x8)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_addToFM_C22(Char(Zero), x0, x1, x2, x3, x4, x5)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT0(x0, x1)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_primPlusNat3
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT5(EmptyFM, x0, x1)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_splitLT24(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat4(Zero)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch4(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_addToFM00(x0, x1, x2)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat1(x0)
new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_addToFM_C3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_primPlusInt(Neg(x0), Neg(x1))
new_mkVBalBranch3MkVBalBranch182(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT23(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11)
new_primPlusInt(Neg(x0), Pos(x1))
new_primPlusInt(Pos(x0), Neg(x1))
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_splitGT5(Branch(Char(Zero), x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitGT3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat2(Zero)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_primPlusInt(Pos(x0), Pos(x1))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)

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

↳ 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof

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

new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Zero, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Succ(zzz16100), ca, cb) → new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, zzz16090, zzz16100, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, zzz10210, zzz10220, h, ba)
new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Zero, Zero, h, ba) → new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Zero, bg, bh) → new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Succ(zzz13440), bb, bc) → new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz13430, zzz13440, bb, bc)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, Branch(zzz4160, zzz4161, zzz4162, zzz4163, zzz4164), zzz417, cc, cd) → new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, zzz4160, zzz4161, zzz4162, zzz4163, zzz4164, cc, cd)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Zero, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Zero, ca, cb) → new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Zero, ca, cb) → new_intersectFM_C2IntersectFM_C18(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT23(Char(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Succ(zzz83000)), zzz831, zzz832, zzz833, zzz834, be, bf) → new_intersectFM_C2IntersectFM_C16(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz83000, zzz831, zzz832, zzz833, zzz834, zzz825, zzz83000, be, bf)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz11520, zzz11530, bg, bh)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C18(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1150, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Zero, bb, bc) → new_intersectFM_C2IntersectFM_C11(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_mkVBalBranch2(zzz3000, zzz31, new_splitGT4(bd), zzz34, bd), zzz44, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C15(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Zero, bb, bc) → new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)

The TRS R consists of the following rules:

new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz2637, dc, dd)
new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1052, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb) → new_addToFM_C10(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz1837), Succ(zzz1832), eb)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, dg)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkVBalBranch5(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz26370, zzz26371, zzz26373, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz231430, zzz231431, zzz26374, zzz231434, dc, dd), dc, dd)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), db) → new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28240), dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28240, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBalBranch(zzz2484, zzz2485, zzz2487, new_mkVBalBranch2(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), dg), ty_Char, dg)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), dg) → new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Succ(zzz253500), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz253500, db)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, EmptyFM, dc, dd) → error([])
new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1051, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_addToFM_C4(Branch(zzz730, zzz731, zzz732, zzz733, zzz734), zzz54, bd) → new_addToFM_C22(zzz730, zzz731, zzz732, zzz733, zzz734, zzz54, bd)
new_splitLT0(zzz3000, zzz31, zzz32, zzz34, bd) → new_splitLT40(bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(new_primPlusNat1(zzz1130, zzz8200)), zzz7200, bd)
new_splitGT5(EmptyFM, cc) → new_splitGT4(cc)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Pos(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz25400, dg)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28010), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), db) → new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, db)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27850), dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27850, dc, dd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28220), zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28220, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), dg) → new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, dg)
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg), dg)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Zero, zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT24(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), dg) → new_mkBalBranch(zzz2489, zzz2490, new_mkVBalBranch2(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, dg), zzz2493, ty_Char, dg)
new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd) → new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, bd)
new_addToFM0(zzz34, zzz3000, zzz31, bd) → new_addToFM_C3(zzz34, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_addToFM_C3(EmptyFM, zzz3000, zzz31, bd) → Branch(Char(Succ(zzz3000)), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8350), bd) → new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8350, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd)
new_mkBranch(zzz2812, zzz2813, zzz2814, zzz2815, zzz2816, eg, eh) → Branch(zzz2813, zzz2814, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM(zzz2815, eg, eh)), new_sizeFM(zzz2816, eg, eh)), zzz2815, zzz2816)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz2793000, zzz280700, dc, dd)
new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Zero)), zzz2314340, zzz2314341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz231430, zzz231431, zzz2637, zzz2314343, dc, dd), zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz2791000, zzz279500, dc, dd)
new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Succ(zzz16430), df) → new_mkBalBranch(zzz1636, zzz1637, new_mkVBalBranch6(zzz1641, zzz1631, zzz1632, Neg(Succ(zzz1633)), zzz1634, zzz1635, zzz1639, df), zzz1640, ty_Char, df)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd) → zzz33
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, zzz582, zzz583, zzz584), EmptyFM, bd) → new_addToFM0(Branch(zzz580, zzz581, zzz582, zzz583, zzz584), zzz3000, zzz31, bd)
new_mkVBalBranch4(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, bd)
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, EmptyFM, zzz231434, dc, dd) → error([])
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2784, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27880), zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz27880, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28050), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, dg)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitLT5(Branch(Char(Zero), zzz821, zzz822, zzz823, zzz824), zzz825, be)
new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de) → new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), de)
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da) → Branch(Char(Succ(zzz2464)), new_addToFM00(zzz2460, zzz2465, da), zzz2461, zzz2462, zzz2463)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Succ(zzz17840), ea) → new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, zzz17830, zzz17840, ea)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Succ(zzz13000), dh) → new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, zzz12990, zzz13000, dh)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Zero, da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Succ(zzz28170), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz28170, dc, dd)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2821, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_splitGT4(bd) → new_emptyFM(bd)
new_mkVBalBranch7(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, bd)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Succ(zzz21020), ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, EmptyFM, zzz231434, dc, dd) → error([])
new_mkVBalBranch8(zzz2674, Branch(zzz26680, zzz26681, zzz26682, zzz26683, zzz26684), zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_mkVBalBranch30(zzz2674, zzz26680, zzz26681, zzz26682, zzz26683, zzz26684, zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, ec)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Succ(zzz16430), df) → new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, zzz16420, zzz16430, df)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Succ(zzz21020), ce) → new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, zzz21010, zzz21020, ce)
new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2494)), zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg)
new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2818, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_splitGT0(zzz4000, bd) → new_splitGT40(zzz4000, bd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_primPlusInt(Neg(zzz23240), Neg(zzz23180)) → Neg(new_primPlusNat1(zzz23240, zzz23180))
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28080), zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28080, zzz279300, dc, dd)
new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_mkVBalBranch2(zzz404, zzz405, new_splitGT5(zzz407, cc), zzz408, cc)
new_splitLT40(bd) → new_emptyFM(bd)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea) → zzz1781
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz266200)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be)
new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg) → new_splitGT10(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz1526), Succ(zzz1521), cg)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd) → new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd)
new_mkVBalBranch7(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch8(zzz2674, EmptyFM, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_addToFM(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), db) → new_mkBalBranch(zzz2474, zzz2475, new_mkVBalBranch2(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, db), zzz2478, ty_Char, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd) → new_addToFM_C4(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, bd)
new_splitLT41(zzz4000, bd) → new_emptyFM(bd)
new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz231434, dc, dd)
new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce) → zzz2098
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef), ef)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT5(EmptyFM, zzz581, ef) → new_splitLT41(zzz581, ef)
new_addToFM00(zzz71, zzz54, bd) → zzz54
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_splitLT5(Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, Branch(zzz23143430, zzz23143431, zzz23143432, zzz23143433, zzz23143434), zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz23143430, zzz23143431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz231430, zzz231431, zzz2637, zzz23143433, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz2314340, zzz2314341, zzz23143434, zzz2314344, dc, dd), dc, dd)
new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd) → new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Succ(zzz15280), cg) → new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, zzz15270, zzz15280, cg)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_primMinusNat0(Succ(zzz232400), Zero) → Pos(Succ(zzz232400))
new_sizeFM(EmptyFM, ed, ee) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Succ(zzz254000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz254000, dg)
new_primMulNat2(Succ(zzz279400)) → new_primPlusNat1(new_primPlusNat1(Zero, Succ(zzz279400)), Succ(zzz279400))
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Zero, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch7(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Neg(zzz25350), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2688, Branch(zzz2678, zzz2679, Neg(Succ(zzz2680)), zzz2681, zzz2682), Branch(zzz2683, zzz2684, Neg(Succ(zzz2685)), zzz2686, zzz2687), ty_Char, cf)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz253800), zzz25280, db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, db)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, bd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28030), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz28030, dc, dd)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz254200), zzz25320, dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, dg)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2799, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Succ(zzz26760), ec) → new_mkBalBranch(zzz2664, zzz2665, zzz2667, new_mkVBalBranch8(zzz2674, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec), ty_Char, ec)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), EmptyFM, zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT41(zzz581, ef), ef)
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz3120, zzz3121, zzz3122, zzz3123, zzz3124), bd) → new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27900), dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz27900, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253900, Zero, db)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), db) → new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz17250), df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Succ(zzz17250), df)
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2788, dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, zzz2788, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28230), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2796, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_primMulNat(Zero) → Zero
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT25(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, bd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBalBranch(zzz2469, zzz2470, zzz2472, new_mkVBalBranch2(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), db), ty_Char, db)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Succ(zzz17840), ea) → new_mkVBalBranch2(zzz1777, zzz1778, new_splitGT3(zzz1780, zzz1782, ea), zzz1781, ea)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_addToFM_C4(EmptyFM, zzz54, bd) → Branch(Char(Zero), zzz54, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_primPlusInt(Pos(zzz23240), Neg(zzz23180)) → new_primMinusNat0(zzz23240, zzz23180)
new_primPlusInt(Neg(zzz23240), Pos(zzz23180)) → new_primMinusNat0(zzz23180, zzz23240)
new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh) → new_splitLT10(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz1298), Succ(zzz1293), dh)
new_splitGT3(Branch(Char(Succ(zzz824000)), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT24(zzz824000, zzz8241, zzz8242, zzz8243, zzz8244, zzz825, zzz825, zzz824000, be)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_splitGT5(Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT23(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, EmptyFM, zzz2314344, dc, dd) → error([])
new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch5(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Succ(zzz28070), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, zzz28070, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), bd)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Zero, df)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8540), bd) → new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8540, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2800, dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, zzz2800, zzz279100, dc, dd)
new_addToFM_C22(Char(Succ(zzz7000)), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → new_mkBalBranch(Char(Succ(zzz7000)), zzz71, new_addToFM_C4(zzz73, zzz54, bd), zzz74, ty_Char, bd)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Succ(zzz18400), eb) → new_mkBalBranch(Char(Succ(zzz1832)), zzz1833, new_addToFM_C3(zzz1835, zzz1837, zzz1838, eb), zzz1836, ty_Char, eb)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, zzz8200, bd)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254400, Zero, dg)
new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitLT24(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_splitGT5(Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT26(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Succ(Zero), zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitLT5(Branch(Char(Succ(zzz1006)), zzz1007, zzz1008, zzz1009, zzz1010), zzz1011, h)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25420, zzz25320, dg)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Zero, cg) → new_splitGT3(zzz1525, zzz1526, cg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkVBalBranch2(zzz3000, zzz31, EmptyFM, zzz34, bd) → new_addToFM0(zzz34, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2674, Branch(zzz2664, zzz2665, Pos(Succ(zzz2666)), zzz2667, zzz2668), Branch(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673), ty_Char, ec)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Zero, ce) → new_mkVBalBranch2(zzz2095, zzz2096, zzz2098, new_splitLT5(zzz2099, zzz2100, ce), ce)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, new_primPlusInt(new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)), dc, dd)
new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Succ(zzz26620000)))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28190), dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz28190, dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28060), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28060, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2822, dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2822, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), db) → new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz2739000, zzz278300, dc, dd)
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Succ(zzz7200), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_splitGT3(Branch(Char(Zero), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT27(zzz8241, zzz8242, zzz8243, zzz8244, zzz825, be)
new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd)
new_splitGT3(EmptyFM, zzz825, be) → new_splitGT40(zzz825, be)
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, Branch(zzz263740, zzz263741, zzz263742, zzz263743, zzz263744), zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz263740, zzz263741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz26370, zzz26371, zzz26373, zzz263743, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz231430, zzz231431, zzz263744, zzz231434, dc, dd), dc, dd)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Succ(zzz24670), da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, db)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz16290), de) → new_mkBalBranch(zzz1622, zzz1623, new_mkVBalBranch6(zzz1627, zzz1617, zzz1618, Pos(Succ(zzz1619)), zzz1620, zzz1621, zzz1625, de), zzz1626, ty_Char, de)
new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2479)), zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db)
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), ed, ee) → zzz21912
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Neg(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, EmptyFM, bd) → new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd)
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitGT24(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, Succ(zzz1011), Succ(zzz1006), h)
new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2787, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Zero, cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_primPlusInt(Pos(zzz23240), Pos(zzz23180)) → Pos(new_primPlusNat1(zzz23240, zzz23180))
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Succ(zzz27950), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz27950, dc, dd)
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, Branch(zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344), dc, dd) → new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_sizeFM(zzz2314343, dc, dd), new_sizeFM(zzz2314344, dc, dd), dc, dd)
new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT3(zzz824, zzz825, be)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), db) → new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27890), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27970), dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27970, dc, dd)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Zero))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_emptyFM(bd) → EmptyFM
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz7980), bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27980), dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz8200, zzz7200, bd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Zero)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Zero, ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), dg) → new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28020), dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz28020, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, bd) → new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), bd)
new_addToFM_C22(Char(Zero), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → Branch(Char(Zero), new_addToFM00(zzz71, zzz54, bd), zzz72, zzz73, zzz74)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd) → zzz34
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_addToFM_C3(Branch(Char(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_addToFM_C23(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bd)
new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, Branch(zzz26370, zzz26371, zzz26372, zzz26373, zzz26374), zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_sizeFM(zzz26374, dc, dd), new_sizeFM(zzz26373, dc, dd), dc, dd)
new_primMinusNat0(Zero, Succ(zzz231800)) → Neg(Succ(zzz231800))
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Succ(zzz26900), cf) → new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, zzz26890, zzz26900, cf)
new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef) → new_splitLT23(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_mkVBalBranch4(zzz55, EmptyFM, zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd)
new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd)
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_splitLT23(Char(Succ(zzz57600)), zzz577, zzz578, zzz579, zzz580, zzz581, ef) → new_splitLT27(zzz57600, zzz577, zzz578, zzz579, zzz580, zzz581, zzz581, zzz57600, ef)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Succ(zzz24670), da) → new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, zzz24660, zzz24670, da)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Succ(zzz16290), de) → new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, zzz16280, zzz16290, de)
new_mkVBalBranch5(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, bd)
new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT23(Char(Zero), zzz577, zzz578, EmptyFM, zzz580, zzz581, ef) → new_addToFM_C4(new_splitLT5(zzz580, zzz581, ef), zzz577, ef)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Succ(zzz26900), cf) → new_mkBalBranch(zzz2678, zzz2679, zzz2681, new_mkVBalBranch4(zzz2688, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, cf), ty_Char, cf)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2809000, zzz281700, dc, dd)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Zero, da) → new_mkBalBranch(Char(Succ(zzz2459)), zzz2460, zzz2462, new_addToFM_C3(zzz2463, zzz2464, zzz2465, da), ty_Char, da)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_primPlusNat1(Zero, Zero) → Zero
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28040), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_primPlusNat3 → Zero
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Succ(zzz26760), ec) → new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, zzz26750, zzz26760, ec)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27860), dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Succ(zzz15280), cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(zzz25350), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz25350, db)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28000), zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz28000, zzz279100, dc, dd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Succ(zzz18400), eb) → new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, zzz18390, zzz18400, eb)
new_splitLT24(zzz404, zzz405, zzz406, EmptyFM, zzz408, cc) → new_splitLT40(cc)
new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, Succ(new_primPlusNat1(zzz1140, zzz8200)), bd)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(zzz25380), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25380, zzz25280, db)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28200), dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_splitGT40(zzz4000, bd) → new_emptyFM(bd)
new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_addToFM_C3(Branch(Char(Zero), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_mkBalBranch(Char(Zero), zzz341, zzz343, new_addToFM_C3(zzz344, zzz3000, zzz31, bd), ty_Char, bd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), zzz279300, dc, dd)
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, db)
new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Succ(zzz13000), dh) → new_splitLT5(zzz1296, zzz1298, dh)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Succ(zzz27830), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz27830, dc, dd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, new_primMulNat2(zzz27940), dc, dd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df) → new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), df)
new_primMinusNat0(Succ(zzz232400), Succ(zzz231800)) → new_primMinusNat0(zzz232400, zzz231800)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT5(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5)
new_primMinusNat0(Zero, Zero)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch32(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch2(x0, x1, EmptyFM, x2, x3)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch32(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5)
new_addToFM_C3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6, x7)
new_splitGT5(EmptyFM, x0)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT26(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_splitLT30(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primPlusNat6(Succ(x0))
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_splitGT3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_splitLT23(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_primPlusNat5(x0)
new_addToFM_C22(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, x5)
new_addToFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_primMulNat(Zero)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT23(Char(Zero), x0, x1, EmptyFM, x2, x3, x4)
new_splitGT27(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_primPlusNat2(Zero)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_mkVBalBranch40(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch5(x0, EmptyFM, x1, x2, x3, x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch7(x0, EmptyFM, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch30(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5)
new_emptyFM(x0)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_primMinusNat0(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7)
new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5)
new_primPlusNat0(Succ(x0))
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_primPlusNat0(Zero)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch8(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, x12)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_splitGT40(x0, x1)
new_primPlusNat6(Zero)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Zero, x4, x5, x6)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch240(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT4(x0, x1, x2, x3, x4)
new_mkVBalBranch8(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, EmptyFM, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT0(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_primPlusNat4(Succ(x0))
new_addToFM0(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_splitLT26(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_splitLT24(x0, x1, x2, Branch(Char(Succ(x3)), x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitLT41(x0, x1)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_splitGT4(x0)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT25(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Succ(x10), x11)
new_splitGT3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT24(x0, x1, x2, Branch(Char(Zero), x3, x4, x5, x6), x7, x8)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_addToFM_C22(Char(Zero), x0, x1, x2, x3, x4, x5)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT0(x0, x1)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_primPlusNat3
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT5(EmptyFM, x0, x1)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_splitLT24(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat4(Zero)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch4(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_addToFM00(x0, x1, x2)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat1(x0)
new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_addToFM_C3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_primPlusInt(Neg(x0), Neg(x1))
new_mkVBalBranch3MkVBalBranch182(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT23(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11)
new_primPlusInt(Neg(x0), Pos(x1))
new_primPlusInt(Pos(x0), Neg(x1))
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_splitGT5(Branch(Char(Zero), x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitGT3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat2(Zero)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_primPlusInt(Pos(x0), Pos(x1))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)

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

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

new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Zero, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Succ(zzz16100), ca, cb) → new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, zzz16090, zzz16100, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, zzz10210, zzz10220, h, ba)
new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Zero, Zero, h, ba) → new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Zero, bg, bh) → new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Succ(zzz13440), bb, bc) → new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz13430, zzz13440, bb, bc)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, Branch(zzz4160, zzz4161, zzz4162, zzz4163, zzz4164), zzz417, cc, cd) → new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, zzz4160, zzz4161, zzz4162, zzz4163, zzz4164, cc, cd)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Zero, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Zero, ca, cb) → new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Zero, ca, cb) → new_intersectFM_C2IntersectFM_C18(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT23(Char(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Succ(zzz83000)), zzz831, zzz832, zzz833, zzz834, be, bf) → new_intersectFM_C2IntersectFM_C16(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz83000, zzz831, zzz832, zzz833, zzz834, zzz825, zzz83000, be, bf)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz11520, zzz11530, bg, bh)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C18(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1150, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Zero, bb, bc) → new_intersectFM_C2IntersectFM_C11(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_mkVBalBranch2(zzz3000, zzz31, new_splitGT4(bd), zzz34, bd), zzz44, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C15(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Zero, bb, bc) → new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)

The TRS R consists of the following rules:

new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be)
new_splitGT3(Branch(Char(Zero), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT27(zzz8241, zzz8242, zzz8243, zzz8244, zzz825, be)
new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT3(zzz824, zzz825, be)
new_splitGT3(Branch(Char(Succ(zzz824000)), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT24(zzz824000, zzz8241, zzz8242, zzz8243, zzz8244, zzz825, zzz825, zzz824000, be)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Zero, cg) → new_splitGT3(zzz1525, zzz1526, cg)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Succ(zzz15280), cg) → new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, zzz15270, zzz15280, cg)
new_splitGT3(EmptyFM, zzz825, be) → new_splitGT40(zzz825, be)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Zero, cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Succ(zzz15280), cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg) → new_splitGT10(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz1526), Succ(zzz1521), cg)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Succ(zzz17840), ea) → new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, zzz17830, zzz17840, ea)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Succ(zzz17840), ea) → new_mkVBalBranch2(zzz1777, zzz1778, new_splitGT3(zzz1780, zzz1782, ea), zzz1781, ea)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea) → zzz1781
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, zzz582, zzz583, zzz584), EmptyFM, bd) → new_addToFM0(Branch(zzz580, zzz581, zzz582, zzz583, zzz584), zzz3000, zzz31, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch2(zzz3000, zzz31, EmptyFM, zzz34, bd) → new_addToFM0(zzz34, zzz3000, zzz31, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkBranch(zzz2812, zzz2813, zzz2814, zzz2815, zzz2816, eg, eh) → Branch(zzz2813, zzz2814, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM(zzz2815, eg, eh)), new_sizeFM(zzz2816, eg, eh)), zzz2815, zzz2816)
new_sizeFM(EmptyFM, ed, ee) → Pos(Zero)
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), ed, ee) → zzz21912
new_primPlusInt(Pos(zzz23240), Neg(zzz23180)) → new_primMinusNat0(zzz23240, zzz23180)
new_primPlusInt(Pos(zzz23240), Pos(zzz23180)) → Pos(new_primPlusNat1(zzz23240, zzz23180))
new_primPlusInt(Neg(zzz23240), Neg(zzz23180)) → Neg(new_primPlusNat1(zzz23240, zzz23180))
new_primPlusInt(Neg(zzz23240), Pos(zzz23180)) → new_primMinusNat0(zzz23180, zzz23240)
new_primMinusNat0(Succ(zzz232400), Zero) → Pos(Succ(zzz232400))
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primMinusNat0(Zero, Succ(zzz231800)) → Neg(Succ(zzz231800))
new_primMinusNat0(Succ(zzz232400), Succ(zzz231800)) → new_primMinusNat0(zzz232400, zzz231800)
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Zero) → Zero
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkBalBranch(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, new_primPlusInt(new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)), dc, dd)
new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz2637, dc, dd)
new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz266200)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Succ(zzz26620000)))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Zero))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Zero)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Zero, zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat(Zero) → Zero
new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2788, dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, zzz2788, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27880), zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz27880, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27970), dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27970, dc, dd)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Succ(Zero), zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2800, dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, zzz2800, zzz279100, dc, dd)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28000), zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz28000, zzz279100, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz2791000, zzz279500, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, EmptyFM, zzz231434, dc, dd) → error([])
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, Branch(zzz26370, zzz26371, zzz26372, zzz26373, zzz26374), zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_sizeFM(zzz26374, dc, dd), new_sizeFM(zzz26373, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_primMulNat2(Succ(zzz279400)) → new_primPlusNat1(new_primPlusNat1(Zero, Succ(zzz279400)), Succ(zzz279400))
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2818, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, EmptyFM, zzz231434, dc, dd) → error([])
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, Branch(zzz263740, zzz263741, zzz263742, zzz263743, zzz263744), zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz263740, zzz263741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz26370, zzz26371, zzz26373, zzz263743, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz231430, zzz231431, zzz263744, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28230), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz26370, zzz26371, zzz26373, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz231430, zzz231431, zzz26374, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28240), dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28240, Zero, dc, dd)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2821, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28200), dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28190), dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz28190, dc, dd)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2822, dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2822, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28220), zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28220, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2809000, zzz281700, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Succ(zzz28170), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz28170, dc, dd)
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28020), dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz28020, Zero, dc, dd)
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2799, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2796, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27980), dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd)
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Succ(zzz27950), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz27950, dc, dd)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28010), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz2739000, zzz278300, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, EmptyFM, dc, dd) → error([])
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, Branch(zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344), dc, dd) → new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_sizeFM(zzz2314343, dc, dd), new_sizeFM(zzz2314344, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), zzz279300, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Succ(zzz28070), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, zzz28070, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz2793000, zzz280700, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, Branch(zzz23143430, zzz23143431, zzz23143432, zzz23143433, zzz23143434), zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz23143430, zzz23143431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz231430, zzz231431, zzz2637, zzz23143433, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz2314340, zzz2314341, zzz23143434, zzz2314344, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, EmptyFM, zzz2314344, dc, dd) → error([])
new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Zero)), zzz2314340, zzz2314341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz231430, zzz231431, zzz2637, zzz2314343, dc, dd), zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28080), zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28080, zzz279300, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28050), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28060), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28060, Zero, dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28040), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28030), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz28030, dc, dd)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27850), dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27850, dc, dd)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2784, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Succ(zzz27830), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz27830, dc, dd)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27890), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2787, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27860), dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27900), dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz27900, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), dg) → new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), dg) → new_mkBalBranch(zzz2489, zzz2490, new_mkVBalBranch2(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, dg), zzz2493, ty_Char, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), dg) → new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25420, zzz25320, dg)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz254200), zzz25320, dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, dg)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBalBranch(zzz2484, zzz2485, zzz2487, new_mkVBalBranch2(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), dg), ty_Char, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2494)), zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg)
new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254400, Zero, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), dg) → new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Pos(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz25400, dg)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Neg(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Succ(zzz254000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz254000, dg)
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat3 → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_addToFM0(zzz34, zzz3000, zzz31, bd) → new_addToFM_C3(zzz34, zzz3000, zzz31, bd)
new_addToFM_C3(EmptyFM, zzz3000, zzz31, bd) → Branch(Char(Succ(zzz3000)), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_addToFM_C3(Branch(Char(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_addToFM_C23(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bd)
new_addToFM_C3(Branch(Char(Zero), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_mkBalBranch(Char(Zero), zzz341, zzz343, new_addToFM_C3(zzz344, zzz3000, zzz31, bd), ty_Char, bd)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Succ(zzz18400), eb) → new_mkBalBranch(Char(Succ(zzz1832)), zzz1833, new_addToFM_C3(zzz1835, zzz1837, zzz1838, eb), zzz1836, ty_Char, eb)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Succ(zzz18400), eb) → new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, zzz18390, zzz18400, eb)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb) → new_addToFM_C10(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz1837), Succ(zzz1832), eb)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Succ(zzz24670), da) → new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, zzz24660, zzz24670, da)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Zero, da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Succ(zzz24670), da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Zero, da) → new_mkBalBranch(Char(Succ(zzz2459)), zzz2460, zzz2462, new_addToFM_C3(zzz2463, zzz2464, zzz2465, da), ty_Char, da)
new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da) → Branch(Char(Succ(zzz2464)), new_addToFM00(zzz2460, zzz2465, da), zzz2461, zzz2462, zzz2463)
new_addToFM00(zzz71, zzz54, bd) → zzz54
new_emptyFM(bd) → EmptyFM
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, bd) → new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), bd)
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), db) → new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, db)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), db) → new_mkBalBranch(zzz2474, zzz2475, new_mkVBalBranch2(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, db), zzz2478, ty_Char, db)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), db) → new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), db) → new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), db) → new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253900, Zero, db)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2479)), zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db)
new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBalBranch(zzz2469, zzz2470, zzz2472, new_mkVBalBranch2(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), db), ty_Char, db)
new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(zzz25380), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25380, zzz25280, db)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz253800), zzz25280, db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, db)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), db) → new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Neg(zzz25350), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(zzz25350), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz25350, db)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Succ(zzz253500), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz253500, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_splitGT40(zzz4000, bd) → new_emptyFM(bd)
new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitLT24(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT24(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT25(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitLT24(zzz404, zzz405, zzz406, EmptyFM, zzz408, cc) → new_splitLT40(cc)
new_splitLT40(bd) → new_emptyFM(bd)
new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd) → zzz33
new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitGT24(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, Succ(zzz1011), Succ(zzz1006), h)
new_splitGT4(bd) → new_emptyFM(bd)
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), EmptyFM, zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT41(zzz581, ef), ef)
new_splitLT23(Char(Zero), zzz577, zzz578, EmptyFM, zzz580, zzz581, ef) → new_addToFM_C4(new_splitLT5(zzz580, zzz581, ef), zzz577, ef)
new_splitLT5(EmptyFM, zzz581, ef) → new_splitLT41(zzz581, ef)
new_addToFM_C4(Branch(zzz730, zzz731, zzz732, zzz733, zzz734), zzz54, bd) → new_addToFM_C22(zzz730, zzz731, zzz732, zzz733, zzz734, zzz54, bd)
new_addToFM_C4(EmptyFM, zzz54, bd) → Branch(Char(Zero), zzz54, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_splitLT5(Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef) → new_splitLT23(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Succ(zzz13000), dh) → new_splitLT5(zzz1296, zzz1298, dh)
new_splitLT23(Char(Succ(zzz57600)), zzz577, zzz578, zzz579, zzz580, zzz581, ef) → new_splitLT27(zzz57600, zzz577, zzz578, zzz579, zzz580, zzz581, zzz581, zzz57600, ef)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Succ(zzz13000), dh) → new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, zzz12990, zzz13000, dh)
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef), ef)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh) → new_splitLT10(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz1298), Succ(zzz1293), dh)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Succ(zzz21020), ce) → new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, zzz21010, zzz21020, ce)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Succ(zzz21020), ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Zero, ce) → new_mkVBalBranch2(zzz2095, zzz2096, zzz2098, new_splitLT5(zzz2099, zzz2100, ce), ce)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Zero, ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce) → zzz2098
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz3120, zzz3121, zzz3122, zzz3123, zzz3124), bd) → new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd)
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, EmptyFM, bd) → new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd)
new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd) → new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd)
new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd) → new_addToFM_C4(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, bd)
new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd) → new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, zzz8200, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, Succ(new_primPlusNat1(zzz1140, zzz8200)), bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Succ(zzz16430), df) → new_mkBalBranch(zzz1636, zzz1637, new_mkVBalBranch6(zzz1641, zzz1631, zzz1632, Neg(Succ(zzz1633)), zzz1634, zzz1635, zzz1639, df), zzz1640, ty_Char, df)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Succ(zzz16430), df) → new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, zzz16420, zzz16430, df)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df) → new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), df)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz17250), df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Succ(zzz17250), df)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Zero, df)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2688, Branch(zzz2678, zzz2679, Neg(Succ(zzz2680)), zzz2681, zzz2682), Branch(zzz2683, zzz2684, Neg(Succ(zzz2685)), zzz2686, zzz2687), ty_Char, cf)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Succ(zzz26900), cf) → new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, zzz26890, zzz26900, cf)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Succ(zzz26900), cf) → new_mkBalBranch(zzz2678, zzz2679, zzz2681, new_mkVBalBranch4(zzz2688, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, cf), ty_Char, cf)
new_mkVBalBranch4(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, bd)
new_mkVBalBranch4(zzz55, EmptyFM, zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(new_primPlusNat1(zzz1130, zzz8200)), zzz7200, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz8200, zzz7200, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch5(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch5(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch5(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz16290), de) → new_mkBalBranch(zzz1622, zzz1623, new_mkVBalBranch6(zzz1627, zzz1617, zzz1618, Pos(Succ(zzz1619)), zzz1620, zzz1621, zzz1625, de), zzz1626, ty_Char, de)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Succ(zzz16290), de) → new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, zzz16280, zzz16290, de)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de) → new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), de)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Succ(zzz26760), ec) → new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, zzz26750, zzz26760, ec)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Succ(zzz26760), ec) → new_mkBalBranch(zzz2664, zzz2665, zzz2667, new_mkVBalBranch8(zzz2674, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec), ty_Char, ec)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2674, Branch(zzz2664, zzz2665, Pos(Succ(zzz2666)), zzz2667, zzz2668), Branch(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673), ty_Char, ec)
new_mkVBalBranch8(zzz2674, Branch(zzz26680, zzz26681, zzz26682, zzz26683, zzz26684), zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_mkVBalBranch30(zzz2674, zzz26680, zzz26681, zzz26682, zzz26683, zzz26684, zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, ec)
new_mkVBalBranch8(zzz2674, EmptyFM, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_addToFM(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Zero, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch7(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Succ(zzz7200), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8540), bd) → new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8540, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1051, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch7(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, bd)
new_mkVBalBranch7(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz7980), bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8350), bd) → new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8350, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1052, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_addToFM_C22(Char(Succ(zzz7000)), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → new_mkBalBranch(Char(Succ(zzz7000)), zzz71, new_addToFM_C4(zzz73, zzz54, bd), zzz74, ty_Char, bd)
new_addToFM_C22(Char(Zero), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → Branch(Char(Zero), new_addToFM00(zzz71, zzz54, bd), zzz72, zzz73, zzz74)
new_splitLT41(zzz4000, bd) → new_emptyFM(bd)
new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitLT5(Branch(Char(Zero), zzz821, zzz822, zzz823, zzz824), zzz825, be)
new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitLT5(Branch(Char(Succ(zzz1006)), zzz1007, zzz1008, zzz1009, zzz1010), zzz1011, h)
new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd) → zzz34
new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_mkVBalBranch2(zzz404, zzz405, new_splitGT5(zzz407, cc), zzz408, cc)
new_splitGT5(EmptyFM, cc) → new_splitGT4(cc)
new_splitGT5(Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT23(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitGT5(Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT26(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd) → new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT5(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5)
new_primMinusNat0(Zero, Zero)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch32(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch2(x0, x1, EmptyFM, x2, x3)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch32(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5)
new_addToFM_C3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6, x7)
new_splitGT5(EmptyFM, x0)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT26(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_splitLT30(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primPlusNat6(Succ(x0))
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_splitGT3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_splitLT23(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_primPlusNat5(x0)
new_addToFM_C22(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, x5)
new_addToFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_primMulNat(Zero)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT23(Char(Zero), x0, x1, EmptyFM, x2, x3, x4)
new_splitGT27(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_primPlusNat2(Zero)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_mkVBalBranch40(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch5(x0, EmptyFM, x1, x2, x3, x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch7(x0, EmptyFM, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch30(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5)
new_emptyFM(x0)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_primMinusNat0(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7)
new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5)
new_primPlusNat0(Succ(x0))
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_primPlusNat0(Zero)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch8(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, x12)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_splitGT40(x0, x1)
new_primPlusNat6(Zero)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Zero, x4, x5, x6)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch240(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT4(x0, x1, x2, x3, x4)
new_mkVBalBranch8(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, EmptyFM, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT0(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_primPlusNat4(Succ(x0))
new_addToFM0(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_splitLT26(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_splitLT24(x0, x1, x2, Branch(Char(Succ(x3)), x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitLT41(x0, x1)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_splitGT4(x0)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT25(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Succ(x10), x11)
new_splitGT3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT24(x0, x1, x2, Branch(Char(Zero), x3, x4, x5, x6), x7, x8)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_addToFM_C22(Char(Zero), x0, x1, x2, x3, x4, x5)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT0(x0, x1)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_primPlusNat3
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT5(EmptyFM, x0, x1)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_splitLT24(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat4(Zero)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch4(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_addToFM00(x0, x1, x2)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat1(x0)
new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_addToFM_C3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_primPlusInt(Neg(x0), Neg(x1))
new_mkVBalBranch3MkVBalBranch182(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT23(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11)
new_primPlusInt(Neg(x0), Pos(x1))
new_primPlusInt(Pos(x0), Neg(x1))
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_splitGT5(Branch(Char(Zero), x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitGT3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat2(Zero)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_primPlusInt(Pos(x0), Pos(x1))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)

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_splitLT0(x0, x1, x2, x3, x4)
new_splitGT0(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ QDP
                                            ↳ QReductionProof
                                              ↳ QDP
                                                ↳ QDPSizeChangeProof

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

new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Zero, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Succ(zzz16100), ca, cb) → new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, zzz16090, zzz16100, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, zzz10210, zzz10220, h, ba)
new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh) → new_intersectFM_C2IntersectFM_C17(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1142), Succ(zzz1147), bg, bh)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Zero, Zero, h, ba) → new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Zero, bg, bh) → new_intersectFM_C2IntersectFM_C19(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Succ(zzz13440), bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Branch(zzz8340, zzz8341, zzz8342, zzz8343, zzz8344), be, bf) → new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz8340, zzz8341, zzz8342, zzz8343, zzz8344, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, EmptyFM, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz412, cc)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Succ(zzz13440), bb, bc) → new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz13430, zzz13440, bb, bc)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz10210), Zero, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Succ(zzz41300)), zzz414, zzz415, Branch(zzz4160, zzz4161, zzz4162, zzz4163, zzz4164), zzz417, cc, cd) → new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, zzz4160, zzz4161, zzz4162, zzz4163, zzz4164, cc, cd)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Zero, ca, cb) → new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Succ(zzz16090), Zero, ca, cb) → new_intersectFM_C2IntersectFM_C18(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1608, ca, cb)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1337, bb)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Zero), zzz831, zzz832, zzz833, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz829, be)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitLT23(Char(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Char(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd)
new_intersectFM_C2IntersectFM_C14(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, Char(Succ(zzz83000)), zzz831, zzz832, zzz833, zzz834, be, bf) → new_intersectFM_C2IntersectFM_C16(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, zzz83000, zzz831, zzz832, zzz833, zzz834, zzz825, zzz83000, be, bf)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, EmptyFM, h, ba) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1014, h)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Zero), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz10194, h, ba)
new_intersectFM_C2IntersectFM_C18(zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, zzz828, zzz829, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be), zzz828, be)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz11520), Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz11520, zzz11530, bg, bh)
new_intersectFM_C2IntersectFM_C11(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C16(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Zero, Succ(zzz11530), bg, bh) → new_intersectFM_C2IntersectFM_C18(zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz1143, zzz1144, zzz1145, zzz1146, zzz1150, bg, bh)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Succ(zzz13430), Zero, bb, bc) → new_intersectFM_C2IntersectFM_C11(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc) → new_intersectFM_C(new_intersectFM_C2Lts(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, bb), zzz1336, bb)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_mkVBalBranch2(zzz3000, zzz31, new_splitGT4(bd), zzz34, bd), zzz44, bd)
new_intersectFM_C(Branch(Char(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C2IntersectFM_C15(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd)
new_intersectFM_C(Branch(Char(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Char(Zero), zzz41, zzz42, zzz43, zzz44), bd) → new_intersectFM_C(new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, Branch(Char(Succ(zzz1019000)), zzz10191, zzz10192, zzz10193, zzz10194), zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1019000, zzz10191, zzz10192, zzz10193, zzz10194, zzz1011, zzz1019000, h, ba)
new_intersectFM_C2IntersectFM_C12(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, h, ba) → new_intersectFM_C2IntersectFM_C10(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, zzz1019, zzz1020, Succ(zzz1011), Succ(zzz1016), h, ba)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C17(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, Zero, Succ(zzz16100), ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1603, ca)
new_intersectFM_C2IntersectFM_C15(zzz404, zzz405, zzz406, zzz407, zzz408, zzz409, zzz410, zzz411, zzz412, Char(Zero), zzz414, zzz415, zzz416, zzz417, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc), zzz411, cc)
new_intersectFM_C2IntersectFM_C10(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, Zero, Zero, bb, bc) → new_intersectFM_C2IntersectFM_C13(zzz1328, zzz1329, zzz1330, zzz1331, zzz1332, zzz1333, zzz1334, zzz1335, zzz1336, zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, bb, bc)
new_intersectFM_C2IntersectFM_C110(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1603, zzz1604, zzz1605, zzz1606, zzz1607, zzz1608, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, ca), zzz1602, ca)
new_intersectFM_C2IntersectFM_C1(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz1017, zzz1018, EmptyFM, zzz1020, Zero, Succ(zzz10220), h, ba) → new_intersectFM_C(new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h), zzz1015, h)

The TRS R consists of the following rules:

new_intersectFM_C2Gts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be)
new_splitGT3(Branch(Char(Zero), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT27(zzz8241, zzz8242, zzz8243, zzz8244, zzz825, be)
new_splitGT27(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitGT3(zzz824, zzz825, be)
new_splitGT3(Branch(Char(Succ(zzz824000)), zzz8241, zzz8242, zzz8243, zzz8244), zzz825, be) → new_splitGT24(zzz824000, zzz8241, zzz8242, zzz8243, zzz8244, zzz825, zzz825, zzz824000, be)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Zero, cg) → new_splitGT3(zzz1525, zzz1526, cg)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz15270), Succ(zzz15280), cg) → new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, zzz15270, zzz15280, cg)
new_splitGT3(EmptyFM, zzz825, be) → new_splitGT40(zzz825, be)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Zero, cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_splitGT24(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Zero, Succ(zzz15280), cg) → new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg)
new_splitGT25(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, cg) → new_splitGT10(zzz1521, zzz1522, zzz1523, zzz1524, zzz1525, zzz1526, Succ(zzz1526), Succ(zzz1521), cg)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Succ(zzz17840), ea) → new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, zzz17830, zzz17840, ea)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Succ(zzz17830), Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Succ(zzz17840), ea) → new_mkVBalBranch2(zzz1777, zzz1778, new_splitGT3(zzz1780, zzz1782, ea), zzz1781, ea)
new_splitGT10(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, Zero, Zero, ea) → new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea)
new_splitGT11(zzz1777, zzz1778, zzz1779, zzz1780, zzz1781, zzz1782, ea) → zzz1781
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, zzz582, zzz583, zzz584), EmptyFM, bd) → new_addToFM0(Branch(zzz580, zzz581, zzz582, zzz583, zzz584), zzz3000, zzz31, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primMulNat1(zzz34200), bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch2(zzz3000, zzz31, EmptyFM, zzz34, bd) → new_addToFM0(zzz34, zzz3000, zzz31, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), bd) → new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, new_primMulNat0(zzz58200), bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Char, bd)
new_mkBranch(zzz2812, zzz2813, zzz2814, zzz2815, zzz2816, eg, eh) → Branch(zzz2813, zzz2814, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM(zzz2815, eg, eh)), new_sizeFM(zzz2816, eg, eh)), zzz2815, zzz2816)
new_sizeFM(EmptyFM, ed, ee) → Pos(Zero)
new_sizeFM(Branch(zzz21910, zzz21911, zzz21912, zzz21913, zzz21914), ed, ee) → zzz21912
new_primPlusInt(Pos(zzz23240), Neg(zzz23180)) → new_primMinusNat0(zzz23240, zzz23180)
new_primPlusInt(Pos(zzz23240), Pos(zzz23180)) → Pos(new_primPlusNat1(zzz23240, zzz23180))
new_primPlusInt(Neg(zzz23240), Neg(zzz23180)) → Neg(new_primPlusNat1(zzz23240, zzz23180))
new_primPlusInt(Neg(zzz23240), Pos(zzz23180)) → new_primMinusNat0(zzz23180, zzz23240)
new_primMinusNat0(Succ(zzz232400), Zero) → Pos(Succ(zzz232400))
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primMinusNat0(Zero, Succ(zzz231800)) → Neg(Succ(zzz231800))
new_primMinusNat0(Succ(zzz232400), Succ(zzz231800)) → new_primMinusNat0(zzz232400, zzz231800)
new_primPlusNat1(Zero, Succ(zzz620)) → Succ(zzz620)
new_primPlusNat1(Succ(zzz7000), Zero) → Succ(zzz7000)
new_primPlusNat1(Succ(zzz7000), Succ(zzz620)) → Succ(Succ(new_primPlusNat1(zzz7000, zzz620)))
new_primPlusNat1(Zero, Zero) → Zero
new_primMulNat0(zzz6200) → Succ(Succ(new_primPlusNat0(zzz6200)))
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, zzz58200, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch226(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz34200, Succ(new_primPlusNat1(zzz3490, zzz58200)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3490), bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch224(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch220(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkBalBranch(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, new_primPlusInt(new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)), dc, dd)
new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz2637, dc, dd)
new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_sizeFM(zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz266200)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Succ(zzz26620000)))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Succ(Zero))), dc, dd) → new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch51(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(Zero)), dc, dd) → new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch5(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Zero, zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch50(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27400), dc, dd)
new_mkBalBranch6MkBalBranch410(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz273900)), Neg(zzz27400), dc, dd) → new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, new_primMulNat(zzz27400), dc, dd)
new_primMulNat(Succ(zzz223300)) → new_primPlusNat1(new_primMulNat0(zzz223300), Succ(zzz223300))
new_primMulNat(Zero) → Zero
new_mkBalBranch6MkBalBranch411(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2788, dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, zzz2788, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27880), zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz27880, zzz273900, dc, dd)
new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz273900, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, new_mkBalBranch6Size_l(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), new_mkBalBranch6Size_r(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Zero), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Neg(Succ(zzz279100)), Neg(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch37(zzz231430, zzz231431, zzz2637, zzz231434, Pos(Zero), Pos(zzz27920), dc, dd) → new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, new_primMulNat(zzz27920), dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch35(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27970), dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27970, dc, dd)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBranch(Succ(Zero), zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch38(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch33(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2800, dc, dd) → new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, zzz2800, zzz279100, dc, dd)
new_mkBalBranch6MkBalBranch34(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28000), zzz279100, dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz28000, zzz279100, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz2791000, zzz279500, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2791000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz279500), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, EmptyFM, zzz231434, dc, dd) → error([])
new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, Branch(zzz26370, zzz26371, zzz26372, zzz26373, zzz26374), zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_sizeFM(zzz26374, dc, dd), new_sizeFM(zzz26373, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Succ(zzz280900)), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Neg(Zero), Pos(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, new_primMulNat2(zzz28100), dc, dd)
new_mkBalBranch6MkBalBranch113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Pos(Succ(zzz280900)), Neg(zzz28100), dc, dd) → new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, new_primMulNat2(zzz28100), dc, dd)
new_primMulNat2(Succ(zzz279400)) → new_primPlusNat1(new_primPlusNat1(Zero, Succ(zzz279400)), Succ(zzz279400))
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch119(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2818, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, EmptyFM, zzz231434, dc, dd) → error([])
new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, Branch(zzz263740, zzz263741, zzz263742, zzz263743, zzz263744), zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz263740, zzz263741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz26370, zzz26371, zzz26373, zzz263743, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz231430, zzz231431, zzz263744, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28230), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz26370, zzz26371, zzz26373, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz231430, zzz231431, zzz26374, zzz231434, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28240), dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28240, Zero, dc, dd)
new_mkBalBranch6MkBalBranch1115(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2821, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28200), dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28190), dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz28190, dc, dd)
new_mkBalBranch6MkBalBranch118(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1113(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2822, dc, dd) → new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2822, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz28220), zzz280900, dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz28220, zzz280900, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch112(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch114(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Succ(zzz281700), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz2809000, zzz281700, dc, dd)
new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, Succ(zzz2809000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch117(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch1110(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd) → new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz2817, dc, dd)
new_mkBalBranch6MkBalBranch116(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, Succ(zzz28170), dc, dd) → new_mkBalBranch6MkBalBranch111(zzz231430, zzz231431, zzz26370, zzz26371, zzz26372, zzz26373, zzz26374, zzz231434, zzz280900, zzz28170, dc, dd)
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch315(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28020), dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz28020, Zero, dc, dd)
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Zero, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch313(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2799, dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch311(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2796, dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch312(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27980), dc, dd) → new_mkBalBranch6MkBalBranch32(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch310(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd) → new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz2795, dc, dd)
new_mkBalBranch6MkBalBranch30(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, Succ(zzz27950), dc, dd) → new_mkBalBranch6MkBalBranch31(zzz231430, zzz231431, zzz2637, zzz231434, zzz279100, zzz27950, dc, dd)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz28010), dc, dd) → new_mkBalBranch6MkBalBranch39(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch314(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch36(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz2739000), Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz2739000, zzz278300, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, Zero, Succ(zzz278300), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd) → new_mkBalBranch6MkBalBranch46(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, EmptyFM, dc, dd) → error([])
new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, Branch(zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344), dc, dd) → new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_sizeFM(zzz2314343, dc, dd), new_sizeFM(zzz2314344, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Zero), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Neg(Succ(zzz279300)), Neg(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, new_primMulNat2(zzz27940), zzz279300, dc, dd)
new_mkBalBranch6MkBalBranch017(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Pos(Succ(zzz279300)), Pos(zzz27940), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, new_primMulNat2(zzz27940), dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, Succ(zzz28070), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz279300, zzz28070, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz2793000, zzz280700, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz2793000), Zero, dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Succ(zzz280700), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, Branch(zzz23143430, zzz23143431, zzz23143432, zzz23143433, zzz23143434), zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz23143430, zzz23143431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz231430, zzz231431, zzz2637, zzz23143433, dc, dd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz2314340, zzz2314341, zzz23143434, zzz2314344, dc, dd), dc, dd)
new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, EmptyFM, zzz2314344, dc, dd) → error([])
new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBranch(Succ(Succ(Zero)), zzz2314340, zzz2314341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz231430, zzz231431, zzz2637, zzz2314343, dc, dd), zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd) → new_mkBalBranch6MkBalBranch0111(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28080), zzz279300, dc, dd) → new_mkBalBranch6MkBalBranch011(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28080, zzz279300, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28050), dc, dd) → new_mkBalBranch6MkBalBranch014(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch019(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28060), dc, dd) → new_mkBalBranch6MkBalBranch010(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, zzz28060, Zero, dc, dd)
new_mkBalBranch6MkBalBranch0110(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch016(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28040), dc, dd) → new_mkBalBranch6MkBalBranch012(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, dc, dd) → new_mkBalBranch6MkBalBranch015(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, dc, dd)
new_mkBalBranch6MkBalBranch018(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Succ(zzz28030), dc, dd) → new_mkBalBranch6MkBalBranch013(zzz231430, zzz231431, zzz2637, zzz2314340, zzz2314341, zzz2314342, zzz2314343, zzz2314344, Zero, zzz28030, dc, dd)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27850), dc, dd) → new_mkBalBranch6MkBalBranch42(zzz231430, zzz231431, zzz2637, zzz231434, Zero, zzz27850, dc, dd)
new_mkBalBranch6MkBalBranch49(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch40(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2784, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch413(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2783, dc, dd)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Zero, dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, Succ(zzz27830), dc, dd) → new_mkBalBranch6MkBalBranch43(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz27830, dc, dd)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch412(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27890), dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch415(zzz231430, zzz231431, zzz2637, zzz231434, zzz273900, zzz2787, dc, dd) → new_mkBalBranch6MkBalBranch44(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch414(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27860), dc, dd) → new_mkBalBranch6MkBalBranch41(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Zero, dc, dd) → new_mkBalBranch6MkBalBranch45(zzz231430, zzz231431, zzz2637, zzz231434, dc, dd)
new_mkBalBranch6MkBalBranch47(zzz231430, zzz231431, zzz2637, zzz231434, Succ(zzz27900), dc, dd) → new_mkBalBranch6MkBalBranch48(zzz231430, zzz231431, zzz2637, zzz231434, zzz27900, Zero, dc, dd)
new_mkVBalBranch3MkVBalBranch225(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz580, zzz581, Neg(Succ(zzz58200)), zzz583, zzz584), zzz343, bd), zzz344, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Succ(zzz24970), dg) → new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz24960, zzz24970, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz24970), dg) → new_mkBalBranch(zzz2489, zzz2490, new_mkVBalBranch2(zzz2494, zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), zzz2492, dg), zzz2493, ty_Char, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch226(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz24960), Zero, dg) → new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch223(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_mkVBalBranch3MkVBalBranch163(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(zzz25230), dg) → new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_primMulNat(zzz25230), dg)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch173(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25320), dg) → new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Pos(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch180(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25320, Neg(zzz25420), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25420, zzz25320, dg)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz254200), zzz25320, dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254200, zzz25320, dg)
new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz25320, dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBalBranch(zzz2484, zzz2485, zzz2487, new_mkVBalBranch2(zzz2494, zzz2495, zzz2488, Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), dg), ty_Char, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz252900, zzz2540000, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz252900), Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, Succ(zzz2540000), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2494)), zzz2495, Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), Branch(zzz2489, zzz2490, Neg(Succ(zzz2491)), zzz2492, zzz2493), ty_Char, dg)
new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg) → new_mkVBalBranch3MkVBalBranch167(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz254400, Zero, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch178(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254400)), dg) → new_mkVBalBranch3MkVBalBranch149(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Zero, dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Succ(zzz25290), dg) → new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch172(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, dg) → new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, new_sizeFM(Branch(zzz2484, zzz2485, Neg(Succ(zzz2486)), zzz2487, zzz2488), ty_Char, dg), dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch160(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Zero, zzz254100, dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Succ(zzz254100)), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Pos(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch159(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, Neg(Zero), dg) → new_mkVBalBranch3MkVBalBranch161(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Pos(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz25400, dg)
new_mkVBalBranch3MkVBalBranch175(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Neg(zzz25400), dg) → new_mkVBalBranch3MkVBalBranch162(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, dg)
new_mkVBalBranch3MkVBalBranch176(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, Succ(zzz254000), dg) → new_mkVBalBranch3MkVBalBranch164(zzz2484, zzz2485, zzz2486, zzz2487, zzz2488, zzz2489, zzz2490, zzz2491, zzz2492, zzz2493, zzz2494, zzz2495, zzz25290, zzz254000, dg)
new_primPlusNat0(Succ(zzz62000)) → Succ(Succ(new_primPlusNat2(zzz62000)))
new_primPlusNat0(Zero) → Succ(Succ(new_primPlusNat3))
new_primPlusNat3 → Zero
new_primPlusNat2(Succ(zzz620000)) → Succ(Succ(new_primPlusNat4(zzz620000)))
new_primPlusNat2(Zero) → Succ(Succ(new_primPlusNat5(new_primPlusNat3)))
new_primPlusNat5(zzz770) → Succ(Succ(zzz770))
new_primPlusNat4(Succ(zzz6200000)) → Succ(Succ(new_primPlusNat6(zzz6200000)))
new_primPlusNat4(Zero) → Succ(Succ(Succ(Succ(new_primPlusNat1(Succ(Zero), Succ(Zero))))))
new_primPlusNat6(Succ(zzz62000000)) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Succ(zzz62000000))), Succ(Succ(Succ(zzz62000000))))), Succ(Succ(zzz62000000)))), zzz62000000)))
new_primPlusNat6(Zero) → Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero))))
new_addToFM0(zzz34, zzz3000, zzz31, bd) → new_addToFM_C3(zzz34, zzz3000, zzz31, bd)
new_addToFM_C3(EmptyFM, zzz3000, zzz31, bd) → Branch(Char(Succ(zzz3000)), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_addToFM_C3(Branch(Char(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_addToFM_C23(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bd)
new_addToFM_C3(Branch(Char(Zero), zzz341, zzz342, zzz343, zzz344), zzz3000, zzz31, bd) → new_mkBalBranch(Char(Zero), zzz341, zzz343, new_addToFM_C3(zzz344, zzz3000, zzz31, bd), ty_Char, bd)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Succ(zzz18400), eb) → new_mkBalBranch(Char(Succ(zzz1832)), zzz1833, new_addToFM_C3(zzz1835, zzz1837, zzz1838, eb), zzz1836, ty_Char, eb)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Zero, Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Succ(zzz18400), eb) → new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, zzz18390, zzz18400, eb)
new_addToFM_C23(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz18390), Zero, eb) → new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb)
new_addToFM_C24(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, eb) → new_addToFM_C10(zzz1832, zzz1833, zzz1834, zzz1835, zzz1836, zzz1837, zzz1838, Succ(zzz1837), Succ(zzz1832), eb)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Succ(zzz24670), da) → new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, zzz24660, zzz24670, da)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Zero, da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Zero, Succ(zzz24670), da) → new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da)
new_addToFM_C10(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, Succ(zzz24660), Zero, da) → new_mkBalBranch(Char(Succ(zzz2459)), zzz2460, zzz2462, new_addToFM_C3(zzz2463, zzz2464, zzz2465, da), ty_Char, da)
new_addToFM_C11(zzz2459, zzz2460, zzz2461, zzz2462, zzz2463, zzz2464, zzz2465, da) → Branch(Char(Succ(zzz2464)), new_addToFM00(zzz2460, zzz2465, da), zzz2461, zzz2462, zzz2463)
new_addToFM00(zzz71, zzz54, bd) → zzz54
new_emptyFM(bd) → EmptyFM
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(new_primPlusNat1(zzz3480, zzz58200)), zzz34200, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch235(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, zzz58200, zzz34200, bd)
new_mkVBalBranch3MkVBalBranch234(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz3000, zzz31, Succ(zzz3480), bd) → new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz3420, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Zero, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch232(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz3000, zzz31, bd) → new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, new_primPlusNat1(new_primMulNat0(zzz34200), Succ(zzz34200)), bd)
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz14720), bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch177(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd)
new_mkVBalBranch3MkVBalBranch150(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Succ(zzz24820), db) → new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz24810, zzz24820, db)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz24820), db) → new_mkBalBranch(zzz2474, zzz2475, new_mkVBalBranch2(zzz2479, zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), zzz2477, db), zzz2478, ty_Char, db)
new_mkVBalBranch3MkVBalBranch235(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz24810), Zero, db) → new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch221(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(zzz25220), db) → new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkVBalBranch3MkVBalBranch140(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(zzz25220), db) → new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_primMulNat(zzz25220), db)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25280), db) → new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch142(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch171(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253900)), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253900, Zero, db)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz2479)), zzz2480, Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), ty_Char, db)
new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkBalBranch(zzz2469, zzz2470, zzz2472, new_mkVBalBranch2(zzz2479, zzz2480, zzz2473, Branch(zzz2474, zzz2475, Pos(Succ(zzz2476)), zzz2477, zzz2478), db), ty_Char, db)
new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db) → new_mkVBalBranch3MkVBalBranch165(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Pos(zzz25380), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch145(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25280, Neg(zzz25380), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25380, zzz25280, db)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz253800), zzz25280, db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz253800, zzz25280, db)
new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz25280, db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Zero, db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch146(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz252600), Succ(zzz2535000), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz252600, zzz2535000, db)
new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, Zero, db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, db) → new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch141(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Succ(zzz25260), db) → new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, new_sizeFM(Branch(zzz2469, zzz2470, Pos(Succ(zzz2471)), zzz2472, zzz2473), ty_Char, db), db)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Neg(zzz25350), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch179(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Pos(zzz25350), db) → new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz25350, db)
new_mkVBalBranch3MkVBalBranch157(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, Succ(zzz253500), db) → new_mkVBalBranch3MkVBalBranch156(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, zzz25260, zzz253500, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch158(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Neg(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Succ(zzz253600)), db) → new_mkVBalBranch3MkVBalBranch147(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Zero, zzz253600, db)
new_mkVBalBranch3MkVBalBranch169(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, Pos(Zero), db) → new_mkVBalBranch3MkVBalBranch170(zzz2469, zzz2470, zzz2471, zzz2472, zzz2473, zzz2474, zzz2475, zzz2476, zzz2477, zzz2478, zzz2479, zzz2480, db)
new_mkVBalBranch3MkVBalBranch227(zzz580, zzz581, zzz58200, zzz583, zzz584, zzz340, zzz341, zzz343, zzz344, zzz3000, zzz31, bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Char, bd)
new_primMulNat1(zzz1031) → new_primPlusNat1(new_primMulNat0(zzz1031), Succ(zzz1031))
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Neg(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch137(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11990), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Zero, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Succ(zzz3000)), zzz31, Branch(zzz580, zzz581, Pos(Zero), zzz583, zzz584), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch174(zzz580, zzz581, zzz583, zzz584, zzz340, zzz341, zzz34200, zzz343, zzz344, zzz3000, zzz31, Succ(zzz11800), bd) → new_mkBalBranch(zzz580, zzz581, zzz583, new_mkVBalBranch2(zzz3000, zzz31, zzz584, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Char, bd)
new_splitGT40(zzz4000, bd) → new_emptyFM(bd)
new_intersectFM_C2Lts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitLT24(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT24(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitLT24(zzz404, zzz405, zzz406, Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), zzz408, cc) → new_splitLT25(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitLT24(zzz404, zzz405, zzz406, EmptyFM, zzz408, cc) → new_splitLT40(cc)
new_splitLT40(bd) → new_emptyFM(bd)
new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd) → zzz33
new_intersectFM_C2Gts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitGT24(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, Succ(zzz1011), Succ(zzz1006), h)
new_splitGT4(bd) → new_emptyFM(bd)
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), EmptyFM, zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT41(zzz581, ef), ef)
new_splitLT23(Char(Zero), zzz577, zzz578, EmptyFM, zzz580, zzz581, ef) → new_addToFM_C4(new_splitLT5(zzz580, zzz581, ef), zzz577, ef)
new_splitLT5(EmptyFM, zzz581, ef) → new_splitLT41(zzz581, ef)
new_addToFM_C4(Branch(zzz730, zzz731, zzz732, zzz733, zzz734), zzz54, bd) → new_addToFM_C22(zzz730, zzz731, zzz732, zzz733, zzz734, zzz54, bd)
new_addToFM_C4(EmptyFM, zzz54, bd) → Branch(Char(Zero), zzz54, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd))
new_splitLT5(Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef) → new_splitLT23(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Succ(zzz13000), dh) → new_splitLT5(zzz1296, zzz1298, dh)
new_splitLT23(Char(Succ(zzz57600)), zzz577, zzz578, zzz579, zzz580, zzz581, ef) → new_splitLT27(zzz57600, zzz577, zzz578, zzz579, zzz580, zzz581, zzz581, zzz57600, ef)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Succ(zzz13000), dh) → new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, zzz12990, zzz13000, dh)
new_splitLT23(Char(Zero), zzz577, zzz578, Branch(zzz5790, zzz5791, zzz5792, zzz5793, zzz5794), Branch(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804), zzz581, ef) → new_mkVBalBranch6(zzz577, zzz5790, zzz5791, zzz5792, zzz5793, zzz5794, new_splitLT30(zzz5800, zzz5801, zzz5802, zzz5803, zzz5804, zzz581, ef), ef)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Zero, Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_splitLT27(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz12990), Zero, dh) → new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh)
new_splitLT26(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, dh) → new_splitLT10(zzz1293, zzz1294, zzz1295, zzz1296, zzz1297, zzz1298, Succ(zzz1298), Succ(zzz1293), dh)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Succ(zzz21020), ce) → new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, zzz21010, zzz21020, ce)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Succ(zzz21020), ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Succ(zzz21010), Zero, ce) → new_mkVBalBranch2(zzz2095, zzz2096, zzz2098, new_splitLT5(zzz2099, zzz2100, ce), ce)
new_splitLT10(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, Zero, Zero, ce) → new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce)
new_splitLT11(zzz2095, zzz2096, zzz2097, zzz2098, zzz2099, zzz2100, ce) → zzz2098
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz3120, zzz3121, zzz3122, zzz3123, zzz3124), bd) → new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd)
new_mkVBalBranch6(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, EmptyFM, bd) → new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd)
new_mkVBalBranch40(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, bd) → new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd)
new_addToFM(zzz330, zzz331, zzz332, zzz333, zzz334, zzz31, bd) → new_addToFM_C4(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, bd)
new_mkVBalBranch30(zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, bd) → new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz332, zzz333, zzz334, zzz3120, zzz3121, zzz3122, zzz3123, zzz3124, zzz31, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz72, zzz73, zzz74, zzz55, new_primMulNat0(zzz8200), bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Neg(Zero), zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Neg(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Pos(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch231(zzz80, zzz81, Pos(Zero), zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz55, Branch(zzz80, zzz81, Pos(Zero), zzz83, zzz84), Branch(zzz70, zzz71, Neg(Zero), zzz73, zzz74), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, zzz8200, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(zzz720), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1140), bd) → new_mkVBalBranch3MkVBalBranch237(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz7200, Succ(new_primPlusNat1(zzz1140, zzz8200)), bd)
new_mkVBalBranch3MkVBalBranch236(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch239(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Succ(zzz16430), df) → new_mkBalBranch(zzz1636, zzz1637, new_mkVBalBranch6(zzz1641, zzz1631, zzz1632, Neg(Succ(zzz1633)), zzz1634, zzz1635, zzz1639, df), zzz1640, ty_Char, df)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Succ(zzz16430), df) → new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, zzz16420, zzz16430, df)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz16420), Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkVBalBranch3MkVBalBranch237(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df)
new_mkVBalBranch3MkVBalBranch233(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, df) → new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, new_primMulNat1(zzz1638), df)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz17250), df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Succ(zzz17250), df)
new_mkVBalBranch3MkVBalBranch148(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1631, zzz1632, zzz1633, zzz1634, zzz1635, zzz1636, zzz1637, zzz1638, zzz1639, zzz1640, zzz1641, Succ(zzz1633), Zero, df)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2688, Branch(zzz2678, zzz2679, Neg(Succ(zzz2680)), zzz2681, zzz2682), Branch(zzz2683, zzz2684, Neg(Succ(zzz2685)), zzz2686, zzz2687), ty_Char, cf)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Succ(zzz26890), Succ(zzz26900), cf) → new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, zzz26890, zzz26900, cf)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Zero, cf) → new_mkVBalBranch3MkVBalBranch139(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, cf)
new_mkVBalBranch3MkVBalBranch138(zzz2678, zzz2679, zzz2680, zzz2681, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, zzz2688, Zero, Succ(zzz26900), cf) → new_mkBalBranch(zzz2678, zzz2679, zzz2681, new_mkVBalBranch4(zzz2688, zzz2682, zzz2683, zzz2684, zzz2685, zzz2686, zzz2687, cf), ty_Char, cf)
new_mkVBalBranch4(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, bd)
new_mkVBalBranch4(zzz55, EmptyFM, zzz70, zzz71, zzz7200, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Succ(zzz7200)), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch238(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz70, zzz71, new_mkVBalBranch6(zzz55, zzz80, zzz81, Neg(Succ(zzz8200)), zzz83, zzz84, zzz73, bd), zzz74, ty_Char, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(new_primPlusNat1(zzz1130, zzz8200)), zzz7200, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Neg(zzz720), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz720, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Succ(zzz7200)), zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz8200, zzz7200, bd)
new_mkVBalBranch3MkVBalBranch228(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, Succ(zzz1130), bd) → new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch222(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch5(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch5(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Pos(Zero), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch5(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Pos(Zero), zzz73, zzz74, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz16290), de) → new_mkBalBranch(zzz1622, zzz1623, new_mkVBalBranch6(zzz1627, zzz1617, zzz1618, Pos(Succ(zzz1619)), zzz1620, zzz1621, zzz1625, de), zzz1626, ty_Char, de)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Succ(zzz16290), de) → new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, zzz16280, zzz16290, de)
new_mkVBalBranch3MkVBalBranch229(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz16280), Zero, de) → new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de)
new_mkVBalBranch3MkVBalBranch240(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, de) → new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, new_primMulNat1(zzz1624), de)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Zero, Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch143(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), de) → new_mkVBalBranch3MkVBalBranch144(zzz1617, zzz1618, zzz1619, zzz1620, zzz1621, zzz1622, zzz1623, zzz1624, zzz1625, zzz1626, zzz1627, Succ(zzz17240), Succ(zzz1619), de)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Succ(zzz26760), ec) → new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, zzz26750, zzz26760, ec)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Succ(zzz26750), Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Succ(zzz26760), ec) → new_mkBalBranch(zzz2664, zzz2665, zzz2667, new_mkVBalBranch8(zzz2674, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec), ty_Char, ec)
new_mkVBalBranch3MkVBalBranch144(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch166(zzz2664, zzz2665, zzz2666, zzz2667, zzz2668, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, zzz2674, ec) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Char(Zero), zzz2674, Branch(zzz2664, zzz2665, Pos(Succ(zzz2666)), zzz2667, zzz2668), Branch(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673), ty_Char, ec)
new_mkVBalBranch8(zzz2674, Branch(zzz26680, zzz26681, zzz26682, zzz26683, zzz26684), zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_mkVBalBranch30(zzz2674, zzz26680, zzz26681, zzz26682, zzz26683, zzz26684, zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, ec)
new_mkVBalBranch8(zzz2674, EmptyFM, zzz2669, zzz2670, zzz2671, zzz2672, zzz2673, ec) → new_addToFM(zzz2669, zzz2670, Pos(Succ(zzz2671)), zzz2672, zzz2673, zzz2674, ec)
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Zero, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch7(zzz55, zzz84, zzz70, zzz71, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch230(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, Succ(zzz7200), zzz73, zzz74, zzz55, bd) → new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primMulNat0(zzz7200), bd)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch168(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8540), bd) → new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8540, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch151(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1051, bd) → new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch152(zzz80, zzz81, zzz8200, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch7(zzz55, Branch(zzz840, zzz841, zzz842, zzz843, zzz844), zzz70, zzz71, zzz73, zzz74, bd) → new_mkVBalBranch30(zzz55, zzz840, zzz841, zzz842, zzz843, zzz844, zzz70, zzz71, Neg(Zero), zzz73, zzz74, bd)
new_mkVBalBranch7(zzz55, EmptyFM, zzz70, zzz71, zzz73, zzz74, bd) → new_addToFM(zzz70, zzz71, Neg(Zero), zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz7980), bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch181(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch182(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Succ(zzz8350), bd) → new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, new_primPlusNat1(zzz8350, zzz7200), bd)
new_mkVBalBranch3MkVBalBranch153(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, Zero, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd) → new_mkBalBranch(zzz80, zzz81, zzz83, new_mkVBalBranch4(zzz55, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, bd), ty_Char, bd)
new_mkVBalBranch3MkVBalBranch154(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, zzz1052, bd) → new_mkVBalBranch3MkVBalBranch155(zzz80, zzz81, zzz83, zzz84, zzz70, zzz71, zzz7200, zzz73, zzz74, zzz55, bd)
new_addToFM_C22(Char(Succ(zzz7000)), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → new_mkBalBranch(Char(Succ(zzz7000)), zzz71, new_addToFM_C4(zzz73, zzz54, bd), zzz74, ty_Char, bd)
new_addToFM_C22(Char(Zero), zzz71, zzz72, zzz73, zzz74, zzz54, bd) → Branch(Char(Zero), new_addToFM00(zzz71, zzz54, bd), zzz72, zzz73, zzz74)
new_splitLT41(zzz4000, bd) → new_emptyFM(bd)
new_intersectFM_C2Lts0(zzz821, zzz822, zzz823, zzz824, zzz825, be) → new_splitLT5(Branch(Char(Zero), zzz821, zzz822, zzz823, zzz824), zzz825, be)
new_intersectFM_C2Lts(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, h) → new_splitLT5(Branch(Char(Succ(zzz1006)), zzz1007, zzz1008, zzz1009, zzz1010), zzz1011, h)
new_splitGT23(zzz31, zzz32, zzz33, zzz34, bd) → zzz34
new_intersectFM_C2Gts1(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc)
new_splitGT26(zzz404, zzz405, zzz406, zzz407, zzz408, cc) → new_mkVBalBranch2(zzz404, zzz405, new_splitGT5(zzz407, cc), zzz408, cc)
new_splitGT5(EmptyFM, cc) → new_splitGT4(cc)
new_splitGT5(Branch(Char(Zero), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT23(zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitGT5(Branch(Char(Succ(zzz407000)), zzz4071, zzz4072, zzz4073, zzz4074), cc) → new_splitGT26(zzz407000, zzz4071, zzz4072, zzz4073, zzz4074, cc)
new_splitLT4(zzz31, zzz32, zzz33, zzz34, bd) → new_splitLT25(zzz31, zzz32, zzz33, zzz34, bd)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT5(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5)
new_primMinusNat0(Zero, Zero)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch32(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch2(x0, x1, EmptyFM, x2, x3)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch32(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5)
new_addToFM_C3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6, x7)
new_splitGT5(EmptyFM, x0)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT26(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12, x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_splitLT30(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primPlusNat6(Succ(x0))
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_splitGT3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_splitLT23(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_primPlusNat5(x0)
new_addToFM_C22(Char(Succ(x0)), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, x5)
new_addToFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_primMulNat(Zero)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT23(Char(Zero), x0, x1, EmptyFM, x2, x3, x4)
new_splitGT27(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_primPlusNat2(Zero)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_mkVBalBranch40(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch5(x0, EmptyFM, x1, x2, x3, x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch7(x0, EmptyFM, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch30(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5)
new_emptyFM(x0)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_primMinusNat0(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7)
new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5)
new_primPlusNat0(Succ(x0))
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Succ(x6)), x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_primPlusNat0(Zero)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch8(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, x12)
new_splitGT24(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_splitGT40(x0, x1)
new_primPlusNat6(Zero)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Zero, x4, x5, x6)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch240(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT4(x0, x1, x2, x3, x4)
new_mkVBalBranch8(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, EmptyFM, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitGT24(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_primPlusNat4(Succ(x0))
new_addToFM0(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Zero, x13)
new_splitLT26(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_splitLT24(x0, x1, x2, Branch(Char(Succ(x3)), x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitLT41(x0, x1)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_splitGT4(x0)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Pos(Zero), x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT25(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_splitGT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Succ(x10), x11)
new_splitGT3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13, x14)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT24(x0, x1, x2, Branch(Char(Zero), x3, x4, x5, x6), x7, x8)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Zero), x6, x7, x8, x9)
new_addToFM_C22(Char(Zero), x0, x1, x2, x3, x4, x5)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_primPlusNat3
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT5(EmptyFM, x0, x1)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Neg(Zero), x2, x3, x4, x5, Neg(Succ(x6)), x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_splitLT10(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_splitLT23(Char(Zero), x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_splitLT27(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_splitLT24(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat4(Zero)
new_splitGT10(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch4(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_addToFM00(x0, x1, x2)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat1(x0)
new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Succ(x13), x14)
new_addToFM_C3(Branch(Char(Zero), x0, x1, x2, x3), x4, x5, x6)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_primPlusInt(Neg(x0), Neg(x1))
new_mkVBalBranch3MkVBalBranch182(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT23(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11)
new_primPlusInt(Neg(x0), Pos(x1))
new_primPlusInt(Pos(x0), Neg(x1))
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_splitGT5(Branch(Char(Zero), x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitGT3(Branch(Char(Succ(x0)), x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_primMulNat2(Zero)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch3MkVBalBranch179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_primPlusInt(Pos(x0), Pos(x1))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_splitLT27(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(x13), x14)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)

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: